Impulse Oscillometric Features and Respiratory System Models Track Small Airway Function in Children

© 2012 Merez et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Impulse Oscillometric Features and Respiratory System Models Track Small Airway Function in Children


Introduction
Asthma is an inflammatory condition of the airways resulting in their hyper-reactivity, generating increased mucus, mucosal swelling and airway smooth muscle contraction all of which contribute to (partial) airway obstruction. The symptoms include chest tightness, coughing and wheezing, and in severe cases shortness of breath and low blood oxygen (1). According to Dorland's medical dictionary small airway impairment (SAI) is a chronic obstructive bronchitis with narrowing of the bronchioles and small bronchi. The term small airways refer to about 7 th to 19 th generation of airways with an inner diameter of about 2 to 0.5 mm. These airways are considered to be an important site of inflammation in asthma and chronic obstructive pulmonary disease (COPD). The atopic manifestation just prior to asthma could be early small airway disease (SAD) and then if inflammation persists, asthma would appear. SAD includes a spectrum of inflammatory and fibrotic pulmonary diseases centered on the small conducting airways.
According to the American Academy of Allergy Asthma & Immunology, Asthma and allergies stroke 1 out of 12 Americans and approximately 25 million Americans (8% of the U.S. population) had asthma in 2009. About 1 in 10 children (10%) had asthma and 1 in 12 adults (8%) had asthma in 2009. For the period 2008-2010, asthma prevalence was higher among children than adults. For the period 2008-2010, asthma prevalence was higher among multiplerace, black, and American Indian or Alaska Native persons than white persons. Asthma costs in the US grew from about $53 billion in 2002 to about $56 billion in 2007, about a 6% increase. Compared with adults, children had higher rates for asthma primary care and emergency department visits, similar hospitalization rates, and lower death rates. Asthma was linked to 3,447 deaths (about 9 per day) in 2007. Internationally asthma has a rising prevalence in low and middle income countries and it is reaching a steady level in high income countries. An estimated 300 million people worldwide suffer from asthma, with 250,000 annual deaths attributed to the disease; almost all of these deaths are avoidable (2).
In Mexico, 10% (approximately 10 million people), of the population suffer from asthma. It is the most common cause of chronic illnesses and emergency hospitalizations in children according to the Mexican College of Allergy, Asthma and Pediatric Pulmonology (3).
Assessment of respiratory function is important in diagnosis and monitoring of asthma and other respiratory diseases in children (4). The pulmonary function test most commonly used to detect asthma is spirometry, which measures the volume of air that can be moved in or out of the lungs as a function of time with rapid and maximal inspiratory and expiratory efforts. This requires a considerable degree of cooperation from the subject, which is difficult to achieve in older children and almost impossible to achieve by younger children. This makes the diagnosis of asthma difficult owing to the lack of objective measurements for younger children (5). Furthermore, it has been reported that some asthmatic patients do not improve spirometrically, despite clinical improvement with treatment (6). This is of concern because if asthma is not appropriately controlled, it can lead to permanent airway damage.
In contrast to forced spirometry, the Forced Oscillation Technique (FOT) superimposes small air pressure perturbations on the natural breathing of a subject to measure lungs mechanics (respiratory impedance). The Impulse Oscillometry System (IOS) measures respiratory impedance by using short pulses (impulses) of air pressure. It has been developed as a patientfriendly lung function test that minimizes demands on the patient and requires only passive cooperation of the patient wearing a nose clip, keeping lips tightly closed about a mouthpiece and breathing normally through the mouth. IOS has been used with success to assess lung function in healthy and asthmatic children and adolescents . In infants and children, reversible airway obstruction and bronchial hyperresponsiveness (BHR) are significant components contributing to the diagnosis of bronchial asthma (27). All this evidence, which will be described in detail, confirms that lung function in children and adolescents is sensitively and accurately assessed by the IOS, before and after bronchodilation. To build upon this evidence and demonstrate the potential enhancements in the clinical utility of IOS, here we present respiratory system Model Parameters and selected IOS features derived from Pre-and Post-bronchodilation data acquired from Anglo and Hispanic children, that offer significant improvements in quantitative evaluation of small airway impairments and assessment of asthma in this population.
In 1991, the American Thoracic Society published guidelines focusing on spirometry as the most widely used lung function test, where they presented Reference Values for spirometric parameters for Caucasian and Black men and women. They also mentioned that it is common practice to interpret the results of lung function tests in relation to Reference Values and in terms of whether or not they are considered to be within the "normal" range (33).
The European Respiratory Society in 1995 published a workshop report (34) about "Reference Values for Residual Volume (RV), Functional Residual Capacity (FRC) and Total Lung Capacity (TLC)" in which it was mentioned that reference values play an important role in establishing whether the measured volumes fall within an expected range for healthy individuals of the same sex, similar stature, age, and other characteristics. They also point out that comparing reference with measured values is fraught with difficulties, as this may result in disease being undetected and as a consequence untreated. It is also mentioned that FRC is the only lung volume that can be measured routinely with accuracy and reliability, and in addition it is stated that attempts have been made to evaluate TLC and RV. In this report reference values (values for healthy subjects) and prediction equations for lung volumes for children and adults are obtained using different techniques like helium dilution and body plethysmography. These values are presented for different heights. However, this report does not include reference values and prediction equations based on the FOT or IOS.
Few studies have been developed to obtain Reference Values for healthy children using the FOT and IOS (35)(36)(37)(38)(39)(40)(41)(42). It is essential to have IOS Reference Values for children, as this technique has been shown to be very effective in the detection of lung abnormalities. Therefore, here we intend to make an effort towards establishing normal IOS Reference Values in North American Anglo and Hispanic children 5 to 19 years old. We also aim to present baseline (pre-) and postbronchodilation IOS parameters for Anglo and Hispanic children with Probable Small Airway Impairment (PSAI), Small Airway Impairment (SAI) and Asthma.
IOS data generate frequency-dependent curves of respiratory impedance (resistance and reactance) that are visually analyzed to recognize changes in their shape and magnitude and distinguish healthy respiratory function from dysfunction. The IOS data can be deployed to develop mechanical and equivalent electrical circuit models of the respiratory impedance to evaluate and quantify lung mechanics. In these equivalent models, electrical components analogous to mechanical resistance, compliance, and inertance inherent in the respiratory system are used. Therefore, estimates for these Model Parameters based on IOS measurements could be used as baseline measures for better detection, diagnosis, and treatment of different respiratory diseases (43).
Previous work by our research group for more than a decade has focused on development and analysis of different equivalent electrical circuit models for human respiratory impedance. This effort to date has demonstrated that the performance of extended Resistance Inductance Capacitance (eRIC) model and the augmented RIC (aRIC) model (an improvement of the eRIC model) ranked in the middle of a series of conventional models developed over the past several decades in terms of total cumulative error. However, they provide parameter estimates that are physiologically more realistic and in line with expected values in normal subjects and those suffering from pulmonary diseases (43)(44)(45)(46)(47)(48)(49)(50)(51), than previous models.
Here we determine the eRIC and aRIC model parameter estimates in addition to sensitive IOS measures of lung function in Normal (N) or Healthy (H), PSAI, SAI and Asthmatic (A), Anglo and Hispanic children. We further evaluate the performance of these models in quantifying lung function in this population and analyze the correlation of these Model Parameters with sensitive IOS measures of lung function.

Pulmonary function tests and previous studies
Pulmonary function refers to how the lungs perform gas exchange. Pulmonary function testing is a practical application of Respiratory Physiology and is necessary for understanding abnormalities in lung function and the effects of treatments. Pulmonary function tests help to determine the severity of functional impairments or defects and the extent to which treatments restore normal function (62). In this section we first review two important pulmonary function tests: Spirometry and Impulse Oscillometry. We then perform a literature review of several studies that have been carried out in previous years to compare several Pulmonary Function Tests (PFTs) to assess the ability of FOT and IOS to measure pulmonary function and to discriminate between impaired and non-impaired conditions.

Spirometry
Spirometry is the most common PFT; it is a measurement of maximal airflow after deep inspiration to fill up the lungs. It can provide information about the size of the breathing tubes (mainly large airways) and about the presence of blockages to airflow (63). The measurements usually obtained from spirometry are (64) The National Asthma Education and Prevention Program (NAEPP) Guidelines previously considered FEV1 as the "gold standard" to assess asthma severity and control, but several studies have suggested that most children have normal or near normal FEV1 even when they are symptomatic. Now the NAEPP has added FEV 1 / FVC ratio as an impairment criterion to classify asthma severity and control. The most important pulmonary function abnormalities seen in asthmatic children are decreases in the FEV 1 / FVC and the FEF25%-75%, while FEV 1 remain in the normal range in spite of asthma severity (65).

Forced Oscillation Technique (FOT)
The fundamental principle of FOT is that respiratory mechanics can be measured from superimposition of external pressure oscillations on the respiratory system during resting breathing (66). Therefore, FOT superimposes small external pressure signals on the natural breathing to determine a subject's breathing mechanics. FOT measures respiratory impedance to this applied forced pressure oscillations produced by a loud speaker (67). FOT is indicated as a reliable diagnostic tool to obtain tidal breathing analysis. One of the great advantages of FOT over other pulmonary function tests is that the results measured are independent of the subject respiratory pattern, therefore it is effort independent; it requires only passive cooperation from the subject breathing normally through a mouth piece, keeping lips airtight closed around it, while wearing a nose clips occluding the nares (68). FOT has been used in humans for more than 50 years; it has been used in children with three major clinical aims (69): 1. To characterize the lung function abnormalities of chronic respiratory diseases in children 2. As a diagnostic tool, especially to recognize asthma and bronchial responsiveness 3. To study the physiological mechanisms and pathophysiology of diverse conditions involving and/or threatening the respiratory system FOT applied at oscillation frequencies between 3 and 35 Hz can provide helpful information to help distinguish between large and small airways. The use of multiple oscillation frequencies in FOT allows a separation of large airways from small airways. Frequencies below 15 Hz, low oscillation frequencies, have been shown to be transmitted more distally (peripherally) in the lungs, whilst frequencies higher than 20 Hz, high oscillation frequencies, can reach only the intermediate size airways. As a result low oscillation frequencies reflect small and large airways, while high oscillation frequencies merely reflect large airways. Therefore, changes in large airway resistance cause uniform changes in resistance at all oscillation frequencies (3-35 Hz), whereas changes in small airway resistance result in noticeable changes in low frequency (3-15 Hz) resistance with small or no change in high frequency resistance. Peripheral airways include all airways with a diameter less than 2mm, and large airways are those with diameters greater than 4 mm (66).
One of the most remarkable features of FOT in relation to spirometry is that it has a relatively greater sensitivity to peripheral airways disease; due to the fact that spirometry does not provide a clear indication of peripheral airway obstruction regardless of the information contained in the flow-volume curve and the values of mid-flow rates (FEF25%-75%) (68).

Impulse Oscillometry System (IOS)
In 1956 Dubois presented the first study on FOT; in this study FOT was applied using sinusoidal oscillations with multiple single frequencies between 2 and 18 Hz. After this study several modifications of FOT were developed, until 1993 when the pulse technique was improved and commercially produced by the German company Jaeger. It was named Impulse Oscillometry System (IOS), as an easier to use method to measure respiratory resistance (R) and reactance (X). The advantages of IOS include good time resolution. It measures 5 pulses per second, with continuous resolution in the frequency domain using a Fourier Integral (65)(66) to calculate respiratory impedance. The IOS, as FOT, superimposes small air pressure perturbations on the natural breathing of a subject to measure the impedance of the respiratory system, offering an easy to use method as it does not require any effort from the subject being tested. An additional advantage is the simplicity of the hardware needed to generate the forced oscillations, allowing smaller, more efficient electronic and mechanical structures with minimal power loss (68).
Some disadvantages of the IOS have to be recognized. The fact that IOS measures spontaneous breathing from a subject allows biological variability, and to counteract this fact multiple tests are required to be performed in a subject in order to establish reliable mean values of IOS parameters. A special aspect of applying pulses of pressure is that they are applied within a very short time causing a higher impact on the respiratory system compared with other lung function tests, and this may be perceived as an unpleasant sensation during the measurements (68).
A Jaeger MasterScreen IOS (Viasys Healthcare, Inc. Yorba Linda, CA, USA) was used in this study. The system was calibrated every day using a 3-L syringe for volume calibrations and a reference resistance (0.2 KPa/L/s) for pressure calibrations. Children were asked to wear a nose clip, while breathing normally through a mouthpiece and were instructed to tightly close their lips around it to avoid air leakage. Three to five IOS test replicates were performed on each subject to ensure reproducible tests without artifacts caused by air leaks, swallowing, breath holding or vocalization (9). In each IOS test impulses were applied for a period of 30 to 45 seconds. IOS data were carefully reviewed off line and quality-assured by our expert clinician to reject segments affected by airflow leak or swallowing artifacts. Coherence was also used as a 'quality assurance index'; it is an index of causality between the input and the output of a linear system, therefore if the system is nonlinear or if it is contaminated by extraneous noise then the coherence is lower than expected. Therefore, measurements with low coherence were excluded in this research to avoid problems with artifacts. Coherence is considered by researchers as a useful guide to quality assurance (67).

IOS parameters
IOS is a multifrequency oscillation method; it provides measures of respiratory mechanics in terms of respiratory impedance as a function of frequency Z (f).
Respiratory Impedance is the transfer function of pressure (P) and flow (Q), derived from the superimposed forced oscillation, after being separated from the respiratory pressure and flow.
The respiratory Impedance (Z) measured by IOS is a complex quantity and consists of a real part called respiratory Resistance (R) and an imaginary part called respiratory Reactance (X).
IOS also includes hallmarks such as Resonant Frequency (Fres) and Reactance Area (AX) also known as the "Goldman Triangle". IOS yields these indices over a selected frequency range of 3 to 35 Hz (68).

A. Impedance Parameters: Respiratory Resistance (R) and Respiratory Reactance (X) a. Respiratory Resistance (R)
The real part of the Impedance (Z) corresponds to the Resistance (R), which includes the resistance of the proximal (central) and distal (peripheral) airways as well as lung tissue and chest wall while these latter resistances are usually negligible. In healthy adult subjects, R is nearly independent of oscillation frequency. When an airway obstruction occurs, either central or peripheral, R5 (Resistance at 5 Hz) is increased above normal values. Central airway obstruction elevates R evenly independent of oscillation frequency. Peripheral airways obstruction is highest at low oscillation frequencies and falls with increasing frequency; this is called the negative frequency-dependence of Resistance (fdR). As peripheral resistance increases, R becomes more frequency dependent. Small children normally present frequency-dependence of resistance, and this may be greater than in adults in the presence of peripheral airflow obstruction. Resistance is measured in cmH2O/L/s or KPa/L/s (68).

b. Respiratory Reactance (X)
The imaginary part of Z, the respiratory Reactance (X), includes the mass-inertive forces of the moving air column expressed in terms of Inertance (I) and the Elastic properties (compliance) of lung periphery expressed as capacitance (C) in electrical terms (68).
C represents the ability of the respiratory system to store energy, primarily located in the lung periphery. The component of X associated with C is defined to be negative in sign. It means C is dominant at low oscillation frequencies, meanwhile the component of X related to I is positive in sign, meaning that I's property is more prominent at high oscillation frequencies (see figure 1). Reactance is measured in cmH2O/L/s or KPa/L/s (68).

B. Other IOS parameters: Resonant Frequency (Fres), Reactance Area (AX) and Frequency dependence of resistance (R5-R25) a. Resonant Frequency
The Resonant Frequency (Fres) is the point at which C and I are equal, therefore reactance is zero and is measured in Hertz (1/s) (68).
This parameter should not be interpreted as a particular respiratory system mechanical property; instead it can be used as a suitable marker to separate low frequency from high frequency impedance. Respiratory system abnormalities cause Fres value to be increased [74].

b. Reactance Area (AX)
The Reactance Area (AX), -the "Goldman Triangle" -was introduced by Michael Goldman in his study on "Clinical applications of forced oscillations" (67); AX is the integrated low frequency respiratory reactance magnitude between 5 Hz and Fres, and is measured in cmH2O/L or KPa/L. AX is a practical FO index related to respiratory compliance. AX is a single quantity that reflects changes in the degree of peripheral airway obstruction and closely correlates with fdR (68). AX is a useful and sensitive index of peripheral airway function (66). Figure 2 shows data collected from a Normal (N) child and a child with Small Airway Impairment (SAI) for this research as an example. In this figure it can be observed that the AX (the Goldman's Triangle) area is bigger for the child with SAI than for the normal child. It is interesting to notice that the values of Fres are very close for both children.
Impulse Oscillometric Features and Respiratory System Models Track Small Airway Function in Children 111

a) Frequency-dependence of resistance (fdR or R5-R20)
It is simply the subtraction of the measured resistance at 20 Hz from the resistance at 5 Hz or 3 Hz. Frequency-dependence of resistance is a characteristic of peripheral airway dysfunction (66).
Changes in AX with treatment interventions parallel changes in frequency-dependence of R. It has been suggested by Goldman et al. (66) that the magnitudes of frequency dependence of R and AX appear to reflect a similarly predominant influence of peripheral airway mechanical function.
Frequency-dependence of resistance occurs in healthy children, and to a better extent in children with respiratory system distresses (67). There is now plenty of evidence that peripheral airway inflammation is present in asthma patients, and frequencydependence of resistance occurs significantly in asthma (68).

Bronchodilation phenotype
The bronchodilation response as a physiological response to short-acting beta agonist medicines has been recommended to demonstrate reversibility of airflow obstruction consistent with the definition of asthma (65).
Bronchoconstriction is defined as increased tone of airway smooth muscles due to inflammation; and bronchodilation is defined as decrease in smooth muscle tone, and as a result a decrease in inflammation. When an increase of airways smooth muscle tone occurs, R increases due to a corresponding decrease in airway lumen. R also increases due to inflammation or edema. In asthmatics, high and low frequency R decreases after bronchodilation, showing a larger decrease in low-frequency R and a resultant decrease in frequency-dependence of resistance. In addition FOT has been reported to demonstrate larger sensitivity to inhaled corticosteroid or to β-agonist inhalation than spirometry (68).
According to a study on PFT in preschool children in 2007, FOT has been successfully performed in different settings, and a number of studies have demonstrated that FOT was capable of identifying airway obstruction and reactions to bronchodilators and bronchoconstrictors (71). Several studies have been developed to assess bronchodilator responses using FOT. Marotta et al. (7) performed a study in 4-year old children concluding that IOS bronchodilator responses are remarkably abnormal in this population (children presented a significant bronchodilator response), and that IOS is a useful diagnostic tool in detection of early asthma development. Oostveen et al. (72) performed a comprehensive review on methodology, recommendations and future developments of FOT in clinical practice stating that FOT is a reliable method to assess bronchial hyperresponsiveness in adults and children. Ortiz et al. (8) performed an IOS study in children 2 to 5 years old in El Paso, Texas, finding that IOS is an acceptable method of assessing airway responses to bronchoactive drugs in this age group. In a more recent study related to the use of FOT to detect bronchodilation in children, Bar-Yishay et al. (73) concluded that FOT could reliably measure response to bronchodilator therapy. Recently Song et al (13) researched the utility of impulse oscillometry in young children with asthma finding that asthmatic children differed from control subjects in IOS-assessed bronchodilator response and that there were some significant correlations between bronchodilator responses of spirometric and IOS parameters. Galant et al. (65) stated that bronchodilator response (BDR) would appear to give important additional information about airway inflammation and found that IOS is a promising test to identify asthmatic preschoolers.
All this evidence confirms that lung function in children and adolescents is sensitively and accurately assessed by IOS, before and after bronchodilation. Nevertheless few longitudinal Forced Oscillation (FO) data exist in healthy subjects or in those with airflow obstruction. Oostveen et al. (72) noted the need for a practical FO index to define airway obstruction. Table 1 provides a summary of several IOS vs Spirometry studies, with their descriptions, different IOS parameters analyzed and conclusions. Table 1 summarizes the utility of different IOS indexes of lung function in relation to spirometric parameters in different subpopulations studied between 2002 and 2009. The conclusions emphasize the necessity to analyze these parameters to determine their efficacy to differentiate between Healthy and Impaired respiratory systems. In our study we focused on the most significant IOS indexes of lung function and pushed the boundary by further analyzing the respiratory impedance Model Parameters to differentiate between Healthy and Impaired respiratory conditions in children.

IOS vs Other techniques
Other researchers have compared IOS with spirometry and other techniques. Table 2 presents a summary of several such studies, with their descriptions, different IOS parameters analyzed and conclusions.

Evaluated Parameters General Conclusions
Olaguibel et al. [18] asthmatics R5, R20, X5 IOS was well accepted for young asthmatic children and     table 3 show the utility of different IOS parameters including the AX, "the Godlman's Triangle", as sensitive measures to assess lung function.

IOS studies
As mentioned before, a number of previous IOS studies, summarized in tables 1, 2 and 3, demonstrate that IOS is able to sensitively and accurately evaluate lung function in children and adolescents, using Pre-and Post-bronchodilation conditions and bronchial challenge. These studies further show that that different IOS parameters at different frequencies serve as quantitative indicators to evaluate the Pre-and Post-bronchodilation response and bronchial challenge results. It is also remarkable that very few studies, only the most recent ones, reported the analysis of the AX parameter, which could offer critical information about lung function in children and adolescents as stated by Goldman et al.  (31). Therefore, here we aim to statistically evaluate the performance of all IOS measured and calculated parameters (Resistances and Reactances, Fres, AX, frequency-dependence of resistance R3-R20 and R5-R20) over 3-35 Hz during pre-post-bronchodilation conditions. We place special emphasis on the previously observed most significant IOS and Model Parameters and will determine which one of these parameters is more effective in differentiating between Pre-and Post-bronchodilation conditions.  Table 4 shows that only few studies have been developed in order to determine Reference IOS Values for children.

IOS reference values -Previous studies
In 1991, the American Thoracic Society published guidelines focusing on spirometry as the most widely used lung function test. This document states that it is common practice to interpret the results of lung function tests in relation to Reference Values and in terms of whether or not they are considered to be within the "normal" range (33).
The European Respiratory Society published a workshop report in 1995 (34) about some commonly measured spirometry parameters such as RV, FRC and TLC. In this document it is stated that reference values play an important role in establishing whether the measured respiratory volumes fall within an expected range for healthy individuals of the same sex, similar stature, age, and other characteristics. In this report reference values (values for healthy subjects) and prediction equations for lung volumes for children and adults are obtained using different techniques like helium dilution and body plethysmography. These values are presented for different heights. However, this report does not include reference values and prediction equations based on the FOT or IOS.
From table 4 we observe that it is crucial to have IOS Reference Values for children. These have been very effective in the detection of lung abnormalities, as demonstrated in table 1, 2, and 3. Therefore, in our research here we attempt to take the first steps towards establishing IOS Reference Values in Healthy North American Anglo and Hispanic children 5 to 19 years old. We also aim to present baseline (pre-) and post-bronchodilation IOS parameter values for this subpopulation of children with Probable Small Airway Impairment (PSAI), Small Airway Impairment (SAI) and Asthma (A).

Respiratory system models
The IOS and FOT impedance curves can be represented by equivalent electrical circuit models of the human respiratory system with components analogous to the resistances, compliances and inertances inherent in the characterization of this system. Respiratory system component values could be estimated using well-established parameter estimation methods. These could then be used to assist physicians in the diagnosis and treatment of different respiratory diseases (43).
In our research we have special interest in the small airways disease (SAD) or small airway impairment (SAI) and asthma. An effective means to characterize small airway dysfunction is by integrating realistic models of lung mechanics based on physiological measurements made by FOT or IOS and other techniques (74).
Different equivalent electrical circuit models with lumped parameter components representing the resistances, inertances, and compliances of the respiratory system have been developed and analyzed over the years by different research groups (44).
Previous work by our research team has focused on development and analysis of six different equivalent electrical circuit models of human respiratory impedance. Our efforts to date, have demonstrated that the performance of the extended RIC (eRIC) and augmented RIC (aRIC) models rank in the middle of a series of conventional models developed over the past several decades in terms of total cumulative error. However, they provide parameter estimates that are physiologically more realistic and in line with expected values in healthy subjects and those suffering from pulmonary diseases than previous models (43)(44)(45)(46)(47)(48)(49)(50)(51).
In the following paragraphs we will introduce the two respiratory system models analyzed in this study: the Extended Resistance-Inertance-Compliance (eRIC) and the Augmented Resistance-Inertance-Compliance (aRIC) models.

a. Extended RIC (eRIC) Model
This model is proposed as an improvement of the RIC model, with an additional Peripheral resistance (Rp) connected in parallel with the capacitance. Therefore, the eRIC model is composed of central (large airway) Resistance (Rc), large airway Inertance (I), peripheral (small airway) Compliance (Cp) and peripheral (small airway) Resistance (Rp). This added Rp allows for the frequency-dependence of resistance observed in impedance data, which is not possible for the RIC model. Rp models the small airways resistance. On the other hand the eRIC model can be also considered as a simplification of either DuBois' (with It equal to zero and Ct equal to infinity) or the Mead's model (with Cl, Cw equal to infinity and Ce equal to zero) (43). The electrical equivalent circuit for the eRIC model is shown in Figure 3:

b. Augmented RIC Model
This model was proposed as an improvement to the eRIC model and it can be considered as a simplification of the Mead's model. aRIC is composed of central (large airway) Resistance (Rc), large airway Inertance (I), peripheral (small airway) Compliance (Cp), peripheral (small airway) Resistance (Rp) and an additional compliance Ce (see figure 4), representing extrathoracic compliance. Its additional capacitance Ce, representing extrathoracic compliance, is thought to increase the real part of the respiratory system's impedance at the higher frequencies due to upper airways shunt effects as observed in IOS data (44). The aRIC impedance is given by:

Parameter estimation technique
Lung properties of a subject can be characterized by determination of the parameters of a respiratory system model that best fits its behavior. This information can then be used, with comparison to Reference Values, to determine underdeveloped features or existence of pathological conditions (55).  Table 5 an example of respiratory system's IOS-based Resistance and Reactance values for a healthy male child (15 years old, 181.6 cm height and 84.1 kg weight) are presented. These IOS data were recorded before and after the use of a bronchodilator (Pre-B and post-B). In Table 6 an example of the Model Parameters calculated for the same child is given.
where 5, 10, 15, 20, 25 f H z  This LS criterion was used to minimize the sum of the squared errors between the measured IOS ZR and Zx and the estimated resistive ZR,est and the estimated reactance Zx,est at frequencies between 5 to 25 Hz (at 5 Hz intervals). The LS criterion was selected due to its commonplace use, its relation with other system identification algorithms and its availability in different software packages (44).
Due to the nonlinear dependence of the aRIC and eRIC impedance functions on the model parameters, the Matlab lsq-nonlin (nonlinear LS) was used in both algorithms, which are based on Newton's Method. Each estimation run began with an initial random guess, a parameter estimate vector produced by a random number generator appropriately weighted. Random initial guesses ranging consistently from 0 to 5, 0 to 0.5, and 0 to 0.05 were used to estimate the values of resistances, capacitances and inductances, respectively.
For each child's averaged IOS data a total of 50 iterations were used to find parameter estimates minimizing the error function, with the Matlab program stopping each time when E (error value) changed by less than a factor of 10 -9 from one iteration to the next one. Therefore, the LS error value at the end provided a measure of the goodness of fit to the given test data for each model (44).

Research method design and statistical analysis
This study was developed as part of a NIH-funded research to perform IOS evaluation of lung function in Anglo and Hispanic children 5-19 years old living in the El Paso, Texas area. The data were collected at Western Sky Medical Research clinic and in a Health Fair held in a Socorro District school over a 3 years period (2006)(2007)(2008). The IOS data collected for this research were quality-assured by our expert clinician and pulmonologist, the late Professor Michael Goldman and were then classified by him into four categories: Normal, Probable Small Airway Impairment (PSAI), Small Airway Impairment (SAI) and Asthma (A).
The data presented in this study were collected in 2008. The data collected were Pre-and Post-bronchodilation data. The date collected analyzed in this study were acquired from 47 children in 2008. Three to five IOS test replicates were performed on each subject to ensure reproducible tests without artifacts caused by air leaks, swallowing, breath holding or vocalization. IOS data were carefully reviewed off line and quality-assured to reject segments affected by airflow leak or swallowing artifacts. A Jaeger MasterScreen IOS (Viasys Healthcare, Inc. Yorba Linda, CA, and USA) was used in this study. The system was calibrated every day before data collection using a 3-L syringe for volume calibrations and a reference resistance (0.2 KPa/L/s) for pressure calibrations. Children were asked to wear a nose clip, while breathing normally through a mouthpiece and were instructed to tightly close their lips around it to avoid air leakage. Children tested using a bronchodilation medicine, called Levalbuterol (Xopenex), were tested (pre-bronchodilation), performing 3 to 5 IOS tests. Then the medicine (Xopenex) was given to the children using a nebulizer for 6 minutes and after that the children were asked to rest for 10 minutes; and finally after this waiting period the children were again tested recording 3 to 5 IOS tests (postbronchodilation).
This research study was supported in part by NIH grant #1 S11 ES013339-01 A1: UTEP-UNM HSC ARCH Program on Border Asthma. The research protocol was approved by the Institutional Review Board of the University of Texas at El Paso. Informed consents were obtained from children over 18 years and the parents or care givers of children under 18 years. A questionnaire on asthma or allergy symptoms provided by the ARCH Program was then completed by the participants or their parents.
Statistical analyses of IOS measured and calculated parameters as well as the eRIC and aRIC model parameters between Pre-and Post-bronchodilation data were made using tdistribution (differences of the means) test and statistical significance was established at a p < 0.05 level.

Results and discussions
The IOS data collected from 47 children in 2008 and Model Parameters calculated from them, under pre-bronchodilation and post-bronchodilation conditions were analyzed. The eRIC and aRIC Model Parameters were calculated over the frequency range of 5 to 25 Hz.
The IOS and Model Parameters selected for analysis were selected from our previous publications as they produced significant results to differentiate between Healthy and Impaired as well as, between Pre-and Post-bronchodilation conditions. These parameters were chosen due to their ability to evaluate respiratory system's properties and impairments. The IOS, eRIC and aRIC Model Parameters analyzed were: R3, R5, R3-R20, R5-R20, X3, X5, AX, Fres, eRIC Cp, eRIC Rp, aRIC Cp and aRIC Rp. In addition to our previous published results, we included IOS parameters at 3 Hz (R3, X3, R3-R20) to our analysis here to evaluate their performance.
After quality assurance by our expert clinician, the collected IOS data from all 47 children were classified into four groups: 6 Healthy (or Normal), 4 PSAI, 11 definite SAI and 24 Asthmatics. Children in these four groups were either Anglo or Hispanic based upon their parent's declarations in the questionnaires. Table 7 for Healthy children, in Table 8 for PSAI children, in Table 9 for children with SAI, and in Table 10 for those with Asthma.  Our expert clinician confirmed that the range of values of all analyzed features: R3, R5, R3-R20, R5-R20, X3, X5, AX, Fres, eRIC Cp, eRIC Rp, aRIC Cp and aRIC Rp obtained for the SAD and Asthmatic groups were comparable to those values he has observed over many years in other asthmatic children of the same age range. Going to increasingly abnormal levels of "diagnostic classification," R3, R5, R5-R20, AX, Fres and Rp continue to increase from Normal to PSAI to SAI to Asthma, while X3, X5 and Cp decreased in this progression. Figures 5,6,7,8,9,10 and 11 show in a more graphical fashion the changes in the most significant IOS and Model Parameters mean values for each of the four groups.       Similarities between Normal and PSAI groups and between SAI and Asthmatic groups were also observed.

Range
From tables 7,8,9, and10 and figures 7,8,9, 10 and 11 we can observe that the most significant IOS and Model Parameters for children classified as Healthy or PSAI were comparable, as these parameters showed a modest difference between these groups. However, these same parameters exhibited clear increases in R3, R5, R3-R20, R5-R20, AX, Fres, and Rp, and a clear decrease in X3, X5 and Cp going from Normal to PSAI. Going to increasingly abnormal levels of "diagnostic classification," R5, R5-R20, AX, Fres and Rp continue to increase from Healthy to PSAI to SAI to Asthmatic conditions, while X5 and Cp decrease in this progression. Differences between SAI and Asthmatic children were also modest.
In the statistical analysis performed for this research comparing Pre-and Post-B IOS and eRIC and aRIC Model Parameters in the Normal or Healthy group, no significant differences were observed (see Table 11).

Pre-B vs Post-B p values
All IOS and Model Parameters >0.05 Table 11. Healthy group p values.
Comparing Pre-and Post-B IOS and eRIC and aRIC Model Parameters for the PSAI group only R3, R35 and eRIC Rc showed significant differences (see Table 12.) Comparing Pre-and Post-B IOS and eRIC and aRIC Model Parameters for the SAI group the following parameters showed significant differences: R3,R5,X3,X5,X10,X15,R3-R20,R5-R20,AX,aRIC Rp, eRIC Rp, eRIC I and eRIC Cp (see Table 13). Comparing Pre-and Post-B IOS, eRIC and aRIC Model Parameters for the Asthmatic group all of the parameters showed significant differences with the exception of aRIC Ce and eRIC I (see Table 14). These selected parameters seem to be sensitive and reliable indices of lung function for respiratory disease classification using Impulse Oscillometric data, eRIC and aRIC Model Parameters.

The correlation coefficient (r) between children Heights and these IOS and Model
Parameters was also analyzed. The parameters showed a good correlation, the best correlation was observed for R5 with R = 0.764, and the lowest r value (0.542) was observed for X5. In Table 15   The statistical correlation between AX and both models' Cps, and R3-R20 and R5-R20 with both models' Rps were also evaluated. The best correlation observed was between AX and eRIC Cp with a value of r = 0.909. The correlation between AX and aRIC Cp had a lower r value equal to 0.760. For the correlation between R3-R20 and eRIC Rp, r was equal to 0.589. The correlation between R5-R20 and eRIC Rp was r = 0.516. For R3-R20 and aRIC Rp, r = 0.787. And finally the correlation between R5-R20 and aRIC Rp was r = 0.731. Figure 12 illustrates the best correlation observed. This was between AX and eRIC Cp.

Conclusions
While expert clinician diagnostic classification distinguished between children based on 4 levels of perceived normality or absence thereof of the visual patterns of IOS data, with the essential features characterizing the differences being associated with abnormalities group mean IOS and the aRIC model data appear to fall into two distinctly different groups: either Normal or Asthmatic, with the essential features characterizing the differences being associated with abnormalities of peripheral airways.
Our present and previous studies (52)(53)(54)(55)(56)(57)(58)(59)(60)(61)75), have demonstrated that equivalent electrical circuit Model Parameters of the human respiratory system are able to track changes in the respiratory system function after bronchodilation. Both the eRIC and aRIC models clearly distinguished between children who were Normal (Healthy) or possibly had mild SAI, who showed no significant changes with bronchodilation-BD), and those who were Asthmatic with SAI, both at baseline and at Pre-to Post-BD conditions. The eRIC model showed an apparently larger peripheral airway compliance (Cp) than the aRIC model, probably because it might include some of the "extrathoracic airway compliance" (Ce). On the other hand, the eRIC model is more parsimonious, and the parameter, Ce, that may be difficult for physicians to understand, appears to show no significant change Post-BD in the Asthmatic group.
It can be observed that children classified as Normal (Healthy) or possible SAI were relatively similar in both IOS and the aRIC model parameters. However, they showed clear increases in R3, R5, R3-R20, R5-R20, AX, Fres, and Rp, and a clear decrease in X3, X5 and Cp going from Normal to PSAI.
Going to increasingly abnormal levels of "diagnostic classification," R3, R5, R5-R20, AX, Fres and Rp continue to increase from Healthy to PSAI to SAI to Asthma, while X3, X5 and Cp decrease in this progression. Differences between SAI and Asthmatic children were modest.
The features used in this work seem to be sensitive and reliable indices for automatic respiratory disease classification using Impulse Oscillometry data. The correlation between AX and the eRIC Cp was the best correlation in both Pre-B and Post-B work.
Our expert clinician confirmed that the range of values of all analyzed features: R3, R5, R3-R20, R5-R20, X3, X5, AX, Fres, eRIC Cp, eRIC Rp, aRIC Cp and aRIC Rp obtained for the SAD and Asthmatic groups were comparable to those values he has observed over many years in other asthmatic children of the same age range.
Comparing all the IOS parameters for Pre-and Post-B data and the eRIC and aRIC Model Parameters in the Normal group, no significant differences were observed. Also comparing Pre-and Post-B parameters for the PSAI group only R3, R5 and the eRIC Rc showed significant differences. Similarly evaluating Pre-and Post-B values for the SAI group, the following parameters showed significant differences: R3, R5, X3, X5, X10, X15, R3-R20, R5-R20, AX, the aRIC Rp, eRIC Rp, eRIC I and eRIC Cp. Finally evaluating Pre-and Post-B values for the Asthmatic group all of the parameters showed significant differences with the exception of the aRIC Ce and eRIC I.
In this research study focusing on children with and without SAI (Healthy), the eRIC Model Parameters showed to be consistent and to some extent more closely correlated with IOS measures compared to the aRIC model parameters. As eRIC is more intuitive, less complex and a more parsimonious model (75), it may be considered a more suitable diagnostic tool for clinical applications than the aRIC model.
IOS lung function data are similarly well-modeled by the eRIC (without upper airway shunt compliance) and aRIC models (with upper airway shunt compliance), which are reduced versions of the popular Mead's model developed at Harvard several decades ago, based on the close correlations of their corresponding parameters excluding Ce. The eRIC model is a more parsimonious and equally powerful model in capturing the differences between SAI and H children, therefore it is recommended as a clinically-preferred model of lung function based on IOS data.
In summary, we conclude that the IOS parameters AX and the eRIC model-derived parameter Cp are the most reliable parameters to track small airway function in children before and after bronchodilation. AX (the "Goldman Triangle"), representing the integrated low frequency respiratory reactance magnitude between 5 Hz and Fres, and the eRIC Cp corresponding to the peripheral (small airway) compliance demonstrated superior diagnostic discrimination compared to all other parameters analyzed and emerged as useful and reliable indices of small airway function in children.
Further work in a larger number of H and SAI children is required to establish normal values for these sensitive indices and enable researchers in this field to perform more effective and timely evaluation, detection, diagnosis, and treatment of different respiratory diseases. Also future work should be performed in order to collect data from a larger sample of children and perform a statistical analysis in order to evaluate IOS parameters and both models (eRIC and aRIC) performances to evaluate these changes in lung function. A definitive choice between the eRIC and aRIC models will require further assessments in a larger sample of children.