Development of Human Respiratory Airway Models: A Review

Development of Human Respiratory Airway Models: A Review

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Development of Human Respiratory Airway Models: A Review Kaveh Ahookhosh, Oveis Pourmehran, Habib Aminfar, Mousa Mohammadpourfard, Mohammad Mohsen Sarafraz PII: DOI: Reference:

S0928-0987(20)30022-1 https://doi.org/10.1016/j.ejps.2020.105233 PHASCI 105233

To appear in:

European Journal of Pharmaceutical Sciences

Received date: Revised date: Accepted date:

15 August 2019 11 January 2020 20 January 2020

Please cite this article as: Kaveh Ahookhosh, Oveis Pourmehran, Habib Aminfar, Mousa Mohammadpourfard, Mohammad Mohsen Sarafraz, Development of Human Respiratory Airway Models: A Review, European Journal of Pharmaceutical Sciences (2020), doi: https://doi.org/10.1016/j.ejps.2020.105233

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Graphical abstract

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Development of Human Respiratory Airway Models: A Review Kaveh Ahookhosha , Oveis Pourmehranb,∗, Habib Aminfara , Mousa Mohammadpourfardc,∗∗, Mohammad Mohsen Sarafrazb a Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran of Mechanical Engineering, The University of Adelaide, Adelaide 5005, Australia c Faculty of Chemical and Petroleum Engineering, University of Tabriz, Iran

b School

Abstract Pulmonary drug delivery has gained great interest as an important subject of research over the past decades given the lung diseases which are affecting millions of people suffer from these diseases. Drug delivery into the respiratory system is influenced by many anatomical and physiological factors such as lung morphometry, breathing patterns, fluid dynamics, particle properties, etc. The respiratory airway structure is one of these parameters which greatly influences the deposition pattern of inhaled drug particles. There have been a wide variety of major morphometric studies, conducted using cadavers to increase an understanding of the respiratory airway anatomy and provide important information for developing realistic airway models. Casting as one of the first methods, was utilized for morphometric studies providing a hollow model for in vitro investigations. The above-mentioned morphometric data were utilized to describe the first idealized airway model as a simple symmetric description of the branching airways, later followed by more realistic asymmetric models. However, even these asymmetric airway models were not good enough to reflect the anatomical complexities of the human respiratory airway and contained several major limitations which made them inefficient. Further attempts alongside with the progress of technology led to introduction of the stochastic and image-based models which provided more realistic and efficient tools for numerical and experimental investigations. The main objective of this study is to provide a comprehensive review about the development of different perspectives of the respiratory airway modeling over the past decades. The following sections will present useful information about anatomy of the human respiratory tract, and different viewpoints of the respiratory airway modeling, including their historical routes, strengths, and deficiencies. Keywords: Respiratory Tract, Airway Models, Particle Deposition, Drug Delivery

Contents

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1 Introduction

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2 The Human Respiratory System 2.1 Anatomy of the Respiratory System . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Physiology of the Respiratory System . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Physical Models 3.1 Respiratory Airway Casts . . 3.1.1 Pre-corrosion Casting Era 3.1.2 Corrosion Casting Era . . 3.2 Plastination . . . . . . . . . . . 3.3 Idealized Respiratory Airway 3.3.1 Symmetrical Models . . . 3.3.2 Asymmetrical Models . .

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∗ Corresponding

author author Email addresses: [email protected] (Oveis Pourmehran), [email protected] (Mousa Mohammadpourfard) ∗∗ Co-corresponding

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Image-based airway models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 CT-based airway models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 MRI-based airway models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Numerical and mathematical models 4.1 Idealized respiratory airway models . 4.2 Stochastic lung models . . . . . . . . . 4.3 Image-based airway models . . . . . . 4.3.1 CT-based airway models . . . . . . 4.3.2 MRI-based airway models . . . . .

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5 Comparison of airway dimensions

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6 Summary and Conclusion

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1. Introduction Lung cancer is a major public health problem and the main cause of 1.4 million death every year, since 2008 [1]. This type of cancer is becoming the leading cause of death among peoples who are dealing with cancer in the western-industrialized countries. In fact, it is deadlier than breast, prostate, colon, liver and kidney cancers [2]. Furthermore, other lung diseases such as asthma, emphysema, pulmonary fibrosis, and pneumonia have affected millions of lives throughout the world and are the third leading cause of death in United States[3]. Aerosolized therapeutics are the most widely used methods for treating and preventing lung diseases. In recent years, due to its advantages, aerosol therapy has been increasingly recognized as an appropriate method for treatment of both pulmonary and non-pulmonary diseases. The oral pathway provides a transfer route, which leads to rapid, nondestructive, and noninvasive drug delivery into the circulation system due to the large lung surface area and excellent blood perfusion. A key advantage of pulmonary drug delivery for treatment of lung diseases is that it enables the delivery of lower doses of aerosolized drugs to the site of action with fewer systemic side-effects in comparison to the circulation system for delivery of drugs. However, for successful pulmonary drug delivery with minimized drug dose and low side-effects, the transfer process has to be targeted. Due to the large number of deaths caused by pulmonary diseases, respiratory drug delivery has been an attractive area of research for the past few decades. A considerable amount of literature has been published on pulmonary drug delivery including several different subjects, such as performance of drug delivery devices (see [4, 5, 6, 7, 8, 9, 10, 11, 12, 13]), the formulation of micro and nano-particles for drug delivery (see [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]), and the magnetic drug targeting (see [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]). Knowledge of particle deposition in human respiratory airway is essential for characterization of the risks of exposure to toxic aerosols, evaluation and development of drug delivery devices, and improvement of treatment methods for chronic respiratory airway diseases. Major challenges such as presentation of a realistic airway model need to be overcome to obtain particle deposition details. Over the past decade, several attempts have been made to present the comprehensive lung airway geometries. Probably the most well-known proposed geometry is Weibels’s model which is simple, and symmetric [41]. Presentation of this model was one of the first steps in development of idealized respiratory airway models and it was used in several different numerical and experimental studies (see [42, 43, 44, 45, 46]). Another extensive morphometric set of data belongs to Raabe et al. (1976) that provides some valuable information in respect to the human bronchial tree [47]. Continuing the path by Weibel and Raabe’s models, several researchers investigated the development of idealized respiratory airway geometries (see [48, 49, 50, 51, 52]). However, because of the complexity of the respiratory airway geometry which has a critical effect on particle deposition, the above-mentioned simple models cannot predict the realistic particle deposition patterns. Recent developments in medical imaging, computed tomography (CT) and magnetic resonance imaging (MRI), have provided an opportunity to reconstruct the respiratory airway tree with all of its anatomical complexities. These realistic airway models have been used for decades in computational fluid dynamics (CFD) and experimental investigations of particle deposition in the respiratory system (see[53, 54, 55, 10, 46, 56, 57, 38]). However, in this technique, capturing the bronchial airway branches are restricted to the large ones due to the low resolution of the CT images, which are caused by vibrations of the subject’s heartbeat and resolution of CT-scanners ([58, 59]). Since it is impossible to model the distal airway generations with CT images numerically, it 3

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is necessary to use appropriate mathematical models. Many studies involving analytical models reported different investigations on particle depositions, gas mixing, and flow distributions (see [60, 61, 50, 62, 63, 64, 65, 66, 67, 68, 69]). As illustrated so far, over the past decades a large number of researchers have elaborated on the particle deposition and pulmonary drug delivery with different modelling perspectives, and now it is obvious that research on this area is a matter of necessity. The major objective of this study is to provide a comprehensive review about the diverse perspectives of respiratory airway modeling and the progress made over the past decades. The content of this review is divided into physical and numericalmathematical categories and in each category, modeling approaches are presented based on chronological classification. The following sections provide necessary background about the human respiratory tract and its anatomical complexities, followed by detailed investigation on airway casts, idealized, image-based and numerical-mathematical models which have been arranged in two major sections. 2. The Human Respiratory System 2.1. Anatomy of the Respiratory System

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The human respiratory system includes several distinct sections including the central nervous system, the chest wall, the pulmonary circulation, and the respiratory tract [70]. The respiratory tract is comprised of three sections, including a complex and repeated network of bifurcations that consists of 23 generations [71]. It looks like an upside down tree, where the thickness and diameter of branches get thinner and thinner with every branching step [72]. Figure 1 1 shows a schematic of these branching airways. The three major categorized sections of the human airways are: (1) extrathoracic (ET) region which includes oral cavity, nasal cavity, pharynx, and larynx to the trachea entrance, (2) tracheobronchial (TB) region which starts from trachea to the terminal bronchioles (generation 16), and (3) acinar (A) region or acinus ranging from generation 17 to 23 ([73, 74]). A detailed schematic of the respiratory system is illustrated in Figure 2 2 . Tracheobronchial region is also called a conducting zone (generations 0-16), which is responsible for conducting the inhaled air to the deep lung. Also, acinar region termed as transitory zone (generations 17-23), and generations 20 to 23 are called respiratory zone [71], where gas exchange takes place. Tracheobronchial (TB) and alveolar (AI) regions are generally called ”intrathoracic (IT) region” [12]. Another common classification is upper and lower respiratory tracts. The upper respiratory tract, like extrathoracic region, includes oral cavity, nasal cavity, pharynx, and larynx. The lower respiratory tract, like intrathoracic region, starts from trachea and covers to the alveolar sacs, which are located almost inside the lungs.

1 Reprinted from Respiratory Physiology & Neurobiology, Vol 148, Ewald R. Weibel, Bernard Sapoval, Marcel Filoche, Design of peripheral airways for efficient gas exchange, Pages 3-21, Copyright (2005), with permission from Elsevier. 2 Reprinted from Journal of Aerosol Science, Vol 42, Werner Hofmann, Modelling inhaled particle deposition in the human ling-A review, Pages 693-724, Copyright (2011), with permission from Elsevier.

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Figure 1: Schematic of the branching airways in Weibel’s model. Reprinted from Weibel et al. (2005) [75], with permission from Elsevier.

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The first parts of the respiratory tract are the nasal and oral cavities, which are followed by nasooropharynx. Pharynx (throat) is a tube-like route for respiratory and digestive systems, with an average length of 12.5 cm [74]. Pharynx includes three different segments: nasopharynx, oropharynx, and laryngopharynx. Nasopharynx is the superior segment of the pharynx, located between the internal nares and soft palate, which is connected to the nasal cavity. Oropharynx is the middle segment of the pharynx, posterior to the mouth and inferior to the soft palate. Naso-oropharynx is a crucial part of the respiratory system, which functions as a filter for large particles and also humidifies the inhaled air. The inferior segment of the pharynx is called laryngopharynx (hypopharynx), which connects larynx to oesophagus. Larynx (voice-box) is a cartilaginous part of the respiratory tract, which is responsible for producing sound and keeping food and drink out of the trachea. The larynx consists of three major cartilaginous pieces, including thyroid cartilage (anterior), epiglottis (superior), and cricoid cartilage (inferior). The thyroid cartilage is the largest piece which makes up the structure of larynx [74]. Epiglottis is a flap of tissue which, with the help of the larynx muscles, makes sure that esophagus gets food and trachea gets air (for more information about the anatomy of the respiratory tract see[71, 70, 12, 76, 77, 78, 74]). A detailed schematic of extra-thoracic region is presented in Figure 3 3 .

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Figure 2: Schematic of the respiratory system. Reprinted from Hofmann (2011) [73], with permission from Elsevier.

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The tracheobronchial tree is the key structure. It starts form trachea, comes along with bronchi and bronchioles and it continues to alveolar sacs. Trachea is a hollow tube with an average length and diameter of 10-14 cm and 1.3-2.7 cm, respectively ([74, 12]), which connects the cricoid cartilage in larynx to the primary bronchi. The stability and strength of the trachea are provided by 16-20 C-shaped cartilaginous rings that also produce the required flexibility for neck movements [74]. These tracheal rings become smaller and less complete along the subsequent branching ([79, 74, 12]).

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Figure 3: Schematic of the extrathoracic region [12]. Reprinted with permission from the author.

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Trachea is divided into the left and right bronchi (primary bronchi) at the carina; however the left bronchus is narrower and longer than the right bronchus (with mean lengths of 5 cm and 2.2 cm respectively), due to the presence of the heart in the left side of the chest and sharing space with the left lung [80, 81]. This branching pattern continues, extending from the primary bronchus to alveolar region. At generation 16, each of terminal bronchioles divides to form the respiratory bronchioles, and it reaches the alveolar sacs after next 6 generations where the gas exchange takes place. The alveolar ducts are the short tubes that connect the respiratory bronchioles to alveolar sacs. At the distal end of each duct an alveolar sac exists, which contains an atrium and several alveoli. Gas exchange takes place at the wall of the alveoli which is surrounded by a network of blood capillaries supplied by the pulmonary artery [74]. Previous studies have reported that the average area of the airways is about 2.5 m2 [82, 72]; while, the total surface area of the alveolar region can be up to 140 m2 [83]. Each adult human lung consists of 300 million alveoli, which provides a 70-80 m2 surface area for gas exchange [74]. However, it should be noted that the presented numbers in this section (e.g. surface areas, number of alveoli, etc.) are not quite accurate and over the years based on different methodologies, various ranges have been proposed for each one. For example, alveolar number is completely related to total lung volume which means with larger lungs, larger number of alveoli is expected. Weibel and Gomez (1962) proposed a geometric model for estimating the number of alveoli in the human lung, which approximately led to 300 million alveoli for most the cases [84]. However, Dunnill (1964, [85]), Angus and Thurlbeck (1972, [86]), and Mercer et al. (1994, [87]) estimated mean numbers of 286, 375, 486 million alveoli in the human lung, respectively. In 2004, Ochs et al. based on a new design-based stereologic approach examined six adult human lungs for estimation of the number of alveoli [88]. The results provided a range between 274 to 790 million alveoli for the examined cases and the mean number of alveoli was 480 million. 2.2. Physiology of the Respiratory System A healthy adult human lungs needs 10-25 m3 air per day to supply the body’s required oxygen. At rest, a 12-20 breathing cycle takes place and each time about 0.5 liters of air is required to complete the 7

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process. The quantity of air for a heavy work can triple this amount, or even more [12]. There are several characteristics describing the volumes and capacities of the respiratory system ([70, 77, 74]): • Inspiratory Reserve Volume (IRV): is the maximum volume of air that can be inhaled during a maximal inspiration. • Expiratory Reserve Volume (ERV): is the maximum volume of air that can be exhaled during a maximal expiration.

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• Residual Volume (RV): is the volume of air in the lung after maximal expiration. • Tidal Volume (TV): is the volume of air which is required for a normal breathing cycle. • Functional Residual Capacity (FRC): is the volume of air in the lung after normal expiration. • Inspiratory Capacity (IC): is the volume which can be inspired after a normal expiration. • Total Lung Capacity (TLC): is the maximum volume of air in the lung.

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• Vital Capacity (VC): is the maximum volume of exchangeable air during inspiration or expiration with the subject’s surroundings. Figure 4 shows a schematic of the above respiratory volumes and capacities.

Figure 4: Respiratory Volumes and Capacities [77].

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In the respiratory system, ventilation, perfusion, and diffusion are the three main physiological functions [70]. The process of inspiration and expiration (breathing cycle) to supply the required air for the alveolus is called ventilation. There are three major pressures involved during the ventilation process; atmospheric pressure, intra-pleural pressure, and intra-alveolar pressure. As it is clear from the names, atmospheric pressure refers to the environmental pressure; while, intra-pleural and intra-alveolar pressures are the pressures inside the pleural cavity and alveoli, respectively ([77, 12]). The intra-pleural pressure is slightly less than the atmospheric and intra-alveolar pressures and it remains at about -4 mm Hg during the process of breathing ([77, 89, 90]). This intra-pleural pressure is the result of two opposing forces during the process. Elastic tissue of the lungs alongside the surface tension of the alveolar fluid pull the lungs inward; meanwhile, a slightly greater outward force created by pleural fluid and thoracic wall working against it, which result in -4 mm Hg pressure. The pressure difference between the intra-pleural and intra-alveolar areas is called transpulmonary pressure. In the respiration process, contraction of diaphragm causes an expansion of the respiratory muscles, which pulls the end of ribs up and expands the volume of the chest cavity. Also, this expansion of the thoracic cavity results in an expansion of the lungs because of the adhesive force of the pleural cavity. Due to the increase in volume of the lungs, the intra-alveolar pressure becomes less than the atmospheric pressure which leads to a pressure difference. The environmental air moves from higher pressure to lower pressure and finally, inspiration takes place. In contrast, during expiration, the respiratory muscles 8

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return to equilibrium, which create a positive pressure that pushes the inhaled air out of the lungs ([12, 70, 77, 74]). During the process of breathing, the lungs are passive, it means they are not responsible for the movements that produce inspiration and expiration. The contraction and relaxation of muscle fibers of both diaphragm and thorax and the adhesive nature of the pleural fluid are the major causes of the breathing process [77]. Figure 5 provides a schematic of lungs for better understanding of the breathing mechanism.

Figure 5: Schematic of the breathing mechanism [77].

3. Physical Models 3.1. Respiratory Airway Casts 185

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The airway structure is one of the main parameters which greatly influence the deposition pattern of inhaled particles. The important anatomical features are airway diameters, lengths, branching angles, and angles of inclination to gravity [91]. Airway casts were one of the earliest choices for replicating anatomical details of the airway structure [92]. In general, cast is a replica that can be produced by injecting solidifying substances into a hallow organ such as lungs, vascular system, etc. Casts are also called as injection replicas [93]. 3.1.1. Pre-corrosion Casting Era Utilizing casts for replicating anatomical features of biological specimens dates back to 14th century where Alessandra Giliani, a master of wax injection techniques, used colored liquids to study the human blood vessels [93]. This path of specimens modeling using wax injection was continued by Andrea del Verrocchio and Leonardo de Vinci for teaching purposes [94]. Several other materials were used including hot water, air, milk, ink, saffron water and, etc. by investigators such as Nicolaus Massa, Johan van Horn, and Reignier de Graaf at the end of 16th century. This period can simply be called pre-corrosion casting era[93].

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3.1.2. Corrosion Casting Era Corrosion casting has been used extensively for replicating different kind of living specimens. This technique involves a solidifiable medium with a low melting point which will be injected to the desired organ and will be allowed to solidify. The invention of the solidifying injection technique is usually referred to Swammerdam (1670), a Dutch naturalist who made major discoveries in anatomy [95]. However, the corrosion casting era perhaps was started with Bidloo investigation (1685), who injected Rose’s metal (a complex alloy of bismuth, lead, and tin) to lungs and then removed its tissue by corrosion technique [95, 96, 97]. The path were followed by Ruysch and Lieberkuhn who injected casting medium to the human organs which led to many superior casts compared to previous ones. The use of acid as a corrosion medium to remove the soft tissues was firstly performed by Lieberkuhn [96]. Afterward, many mediums were used as a solidifying injectant (melted metals, oils, gelatine, shellac, starch, plaster of Paris, glue, etc.) for forming the casts and corrosion agent (hydrochloric acid, potassium hydroxide, formic acid, chromium trioxide, and etc) for removing the surrounding tissues. Nevertheless, casting procedures were laborious which required much time and the replicated specimens were quite brittle. These defects led to a search for finding better materials and casting techniques. In 1935, Schummer for the first time introduced a corrosion resistant polymerizing resin called ”Plastoid” for casting studies. This highly viscous medium was injected into the vascular system by Schummer which resulted in much superior cast compared to the previous studies. Significant technical improvements have been made with introducing a synthetic resin, acrylic resin, as new medium for casting study by Taniguchi et al. (1952, [98]). Afterward, the synthetic resins were extensively utilized by many investigators for replicating different specimens such as lung, liver, ovary, digestive tract and etc. This prospering era of corrosion casting studies was perfectly summarized by Aharinejad and Lametschwandtner (1992, [93]), which is tabulated in table 1. Table 1. Highlights of casting studies used synthetic resins [93]

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Author Taniguchi et al. O.V. Batson Aleksandrowics J. Bugge Goetzen T. Murakami Frasca et al. Nopanitaya et al. Hanstede and Gerrits Amselgruber et al.

Year 1952 1955 1959 1963 1966 1971 1978 1979 1982 1987

Medium injected Acrylic resin Latex Polyester ”Tensol No.7” ”Geon 265” Methylmethacrylate Latexed Batsons No.17 Araldite CY 223 Tradoplast

Target Liver and Kidney Skeletal muscles Various organs Lung Digestive tract Liver Ovary

Figure 6 shows a porcine lung achieved by a corrosion casting technique and acrylic was injected at a very low viscosity into both vascular and airway paths [99]. Most of the earliest casts were built using positive pressure method (see [100, 92, 101]); however, due to the high pressures involved in this technique, risk of distortion or rupture existed. To avoid such a risk, it was necessary to employ a new method for developing silicone rubber casts which is called negative-pressure technique. This method applies a great pressure difference to the distal airways of the bronchial tree at lower pressures compared to a positive-pressure technique which resulted in better filling and less risk of rupture or distortion [102].

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Figure 6: A porcine lung cast alongside with vascular system achieved by corrosion casting technique [99].

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3.2. Plastination In 1977, Gunther von Hagens in his search for a technique to enhance the quality of renal models with utilizing different plastics established basic principles of a new method for replicating specimens called ”Plastination” [103, 104]. Plastination can provide coloured, dry, durable, odorless, and natural looking anatomical specimens of different organs or even whole body. In this method, curable polymers such as silicone, epoxy, or polyester are injected to the intended organ to be replaced with water and lipids of the tissues. The type of the polymer highly depends on the desired properties of the specimens (flexible or firm, opaque or transparent) [103]. There are three types of plastination which can be described as follows [105]: • Whole body/organ plastination: Using this technique, mostly for teaching purposes, organs or even whole body will be preserved.

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• Sheet plastination: In sheet plastination like CT-scan or MRI images, a thin transparent or thick opaque section of body will be preserved. • Luminal cast plastination: In this approach, biological structures such as respiratory branching airways, blood vessels, and ducts can be replicated.

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Plastination also can be utilized alongside with casting to enhance the quality of specimens. Sivrev et al. (1997) used combination of casting and plastination to develop pig eyes for anatomical studies. In their procedure, at first the vitreous chamber of the eye was developed by silicone S10 and then the wall of the eyeball (bulbus oculi) was impregnated with PEG. The procedure was successful and resulted in soft, natural eyes which were safe for handling in anatomical investigations [106]. As a post-casting process, epoxy resins and silicone rubbers are advisable materials for plastiation [97]. 3.3. Idealized Respiratory Airway Models 3.3.1. Symmetrical Models One of the first modern attempts to study the human respiratory airways was carried out by Carson (1820), via a simple postmortem investigation of airway dynamics [107]. There have been a number of 11

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studies (see [108, 109, 110, 111, 112]) including the Carson investigations which formed the first reliable data on the elastic properties of lungs [113]. Investigations on the flow resistance through the branching airways was started by von Recklinghausen (1869) using a very simplified model [114]. In the following investigations of airway resistance, Rohrer (1915) measured the dimensions of the human airway tree down to a diameter of 1 mm which is one of the most complete sets of dimensions data of the human airway tree [115]. In this investigation, diameter and length measurements of the bronchial tree were carried out using a fresh cadaver lung; however, later studies showed that the calculations were only satisfactory in the large branches [41]. Nevertheless, these data sets led to the calculations about pressure decrease, flow rate distribution, and elastic retractive force of the lungs [113]. Furthermore, Rohrer, based on his data, proposed and constructed a dimensional model, which was a starting point in development of morphometric models. Progress continued with the dimensional airway model by Findeisen (1935), in his studies of the deposition of airborne particles in the lung [116]. Findeisen’s model was widely applied since it was the most complete model [117], but the model was not based on sufficient reliable data and most of the bronchial dimensions were not correct [41]. Several other attempts have been made by researchers from 1945 to 1962 (see [118, 119, 120, 121, 122, 123, 124]) to measure the bronchial airway dimensions and propose new morphometric models. A major breakthrough happened in 1963 with Weibel’s morphometric models [41]. Through the morphometric studies, Weibel found out that the Rohrer method was not reliable towards the periphery and his measurements were not in accordance with the Rohrer’s data for branches with less than a 4 mm diameter. Actually, Rohrer underestimated the number branches with less than 4 mm diameter. For example, for branches with 2 mm diameter, Rohrer counted just 86 branches; while, Weibel later reported 300-400 branches. This trend continued for rest of the Rohrer’s work and led to a great underestimation in the number of airways in the entire lung. The defects in the models by Rohrer [115], Findeisen [116] and others convinced Weibel to propose new models based on the regularities and irregularities of respiratory airways. Weibel’s Model: Model ”A” - a Regular Dichotomy Model-A refers to an adult human lung with total air volume of about 4800 ml, where 66% of its volume is devoted to alveoli. It is also worth to notice that only 150 ml of the total volume belongs to the conductive zone. Anatomical measurements were conducted using a resin cast which was an appropriate method for measurements down to generation 5, however dimensions were recorded incompletely down to generation 10. Further dimensional measurements of smaller branches were carried out using histological techniques. In the model-A, Weibel emphasized the regular features of branching airways and assumed that the airway branches multiply toward the periphery by a regular dichotomy (dichotomy=branching into two) [71]. In 1 this model, the average diameters of the branching airways reduce by a factor of 2 3 , which corresponds to Hess-Murray law [125, 126]. Furthermore, trachea dichotomously diverges 19-22 times to the alveolar ducts (ADs) and 23 times to the alveolar sacs (ASs) [127]. In this branching pattern, all elements in a same generation have identical dimensions, which means that the elements branch off their parent with the same diameter, length, and angle (see [128, 71]). Thus, there will be 2n elements in the nth generation [71]. Figure 7 (a)4 shows the schematic of the regular dichotomy in model-A. Table 2 provides some dimensions of the model-A up to generation 5. This Model includes all 23 generations of a real lung, which generally can be grouped into conductive (generations 0 to 16) and transitory (generations 17 to 23) zones. Figure 1 schematically shows the branching airways of model-A. Dimensions of each cylindrical element can be derived by a pair of empirical equations obtained from measurements on cast and histologic properties (see [71]- p.137). In the respiratory region of this model, each alveolus is geometrically characterized by a fraction of a sphere and all ducts and sacs are completely alveolated. Weibel’s ”A” model is one the fundamental models for describing the human respiratory branching airway and a wide variety of experimental and numerical researches were carried out based on this model or used Weibel’s dimensional data for evaluating their works (see [129, 130, 131, 49, 132, 133, 51, 134, 135, 136, 137, 83, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152]). However, this important morphometric model oversimplifies the respiratory airway and includes defects such as: (1) at a given generation, dimensions of all bronchi are identical and the model does not include the necessary asymmetry [153, 150]. (2) branching angles and inclination angles to gravity are not provided [153]. (3) 4 Reprinted from Elsevier Books, edition 1, Ewald R Weibel, Morphometry of the Human Lung, Pages 110-135, Copyright (1963), with permission from Elsevier.

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dimensional data of generations 0-4 are exclusive for every human (see [154, 155, 156, 157, 158, 159]), which were not taken into account [150]. (4) the model does not include any anatomical differences among the lobes, due to the single-path nature of the Weibel’s model [153]. (5) deposition studies on the model showed that particle deposition happen primarily at the carinal ridges, which later CT-based models proved otherwise and showed that particle deposition pattern is more widespread [55].

Figure 7: Schematic of branching patterns in Weibel’s models: (a)Regular dichotomy. (b)Irregular dichotomy. Reprinted from Weibel (1963) [71], with permission from Elsevier.

Table 2. Dimensions of Weibel’s symmetric model (model-A) [160]. Gen G0 G1 G2 G3 G4 G5

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Diameter (mm)) 18 12.2 8.3 5.6 4.5 3.5

Length (mm) 120 47.6 19 7.6 12.7 10.7

Length/Diameter 6.7 3.9 2.3 1.4 2.8 3.1

3.3.2. Asymmetrical Models In nature, the appearance of irregularities in branching patterns, called irregular dichotomy, is more likely. In this branching pattern, the dimensions of the elements in the same generation are mostly unequal. In irregular dichotomy, branching angles are also different, like other dimensions. This difference in dimensions can be so much that daughters may not be distinguished from their parents. This extreme irregularity in branching pattern is called monopody (see [128, 71]). The mammalian tracheobronchial tree includes an asymmetrical branching pattern and the first study that revealed this asymmetrical distribution was carried out by Ross, who investigated the irregular features of a dog’s airway system [161]. Weibel, in the model ”B”, tried to design a more realistic model based on the irregularities of real human lungs. Figure 7 (b)5 illustrates the irregular dichotomy in the Model-B. In this model, Weibel subdivided the lung into nu units, where bronchus of each unit has an equal diameter of D∗ . Also, these units have the same volume and each one includes an equivalent number of alveoli. Figure 8 6 shows the variation in the volume of the units over the airway zones. Unlike Weibel’s ”A” model which is well known and has been used by so many researchers, this model is not popular. 5 Reprinted from Elsevier Books, edition 1, Ewald R Weibel, Morphometry of the Human Lung, Pages 110-135, Copyright (1963), with permission from Elsevier. 6 Reprinted from Elsevier Books, edition 1, Ewald R Weibel, Morphometry of the Human Lung, Pages 136-142, Copyright (1963), with permission from Elsevier.

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Figure 8: Dimensions of the lung units in Weibel’s ”B” model. Reprinted from Weibel (1963) [71], with permission from Elsevier.

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Another asymmetric model based on more morphometric data was developed by Horsfield and Cumming (1968) [48], however, like Weibel’s ”B” model, it has not been considered seriously by researchers for modeling purposes [139]. Unlike all other asymmetrical models, the asymmetric model of Horsfield and Cumming has a different counting system for airway branches, where generations are counted from respiratory zone to trachea as the 25th generation [48]. The lack of interest in using these asymmetrical models may be due to the difficulties exist in utilizing their data for physiological calculations. In both of these asymmetrical models, ”connectivity”, which defines the branching pattern, is unclear [162]. The model of Horsfield et al. (1971) [154] was a further step in development of asymmetrical models and paved the way for more studies (see [163, 164, 165]) on the effects of asymmetry on aerosol deposition patterns in the human respiratory airway. The major breakthrough in the analysis of asymmetry in the conducting airways happened through a morphometric study by Raabe et al. (1976), which investigated parameters like diameters, lengths, and gravity angles in four species of the mammalian lung (human, dog, rat, and hamster) [47]. More information about this model is available in the following paragraph. Yeh and Schum (1980) [49] developed a deterministic model based on the morphometric data by Raabe et al.[47]. The model was a silicone rubber replica cast of the branching airways of the human respiratory system, which was fabricated within the thorax for preserving the exact orientation of the airways. Yeh and Schums’s model consists of different path lengths among the lobes, but the symmetrical pattern of branching through each lobe [49]. Several other studies investigating the effects of asymmetry on inspiratory and expiratory flow conditions have been carried out on asymmetric air passages of the human lung (see [166, 166, 167]). In 1995, Balashazy and Hofmann published a paper in which they analytically and numerically described the effects of asymmetry on the diameter, branching angle, and flow division of respiratory airways for both inspiratory and expiratory flows [168]. They compared their results with the previous experimental studies ([166]), their earlier analytical calculations [167] and numerical simulations [135]. In fact, this study was an extension of their numerical simulations on the symmetric model [135] transferred to the case of an asymmetric model; however, their investigation was limited to a two-generation bifurcation. Also, Zhang et al. (2000) carried out an investigation on the effects of flow rates on aerosol deposition in a symmetric respiratory airways, which included three-generational bifurcation; however, they used a non-uniform outlet pressure to create asymmetric flow rate ratios [169]. Several other researchers have studied particle depositions and air flow patterns in asymmetric airways 14

over the years (see [65, 170, 145, 171, 172, 173]).

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Raabe et al.’s Model: Tracheobronchial Geometry (Human, Dog, Rat, and Hamster) Raabe et al. (1971) began a project entitled ”Respiratory Tract Deposition Models (RTDM)” under the sponsorship of the national institute of environmental health sciences (NIEHS). Their main objective was the development of a respiratory airways model, both physically and mathematically. The purpose was to provide a comprehensive airway model as close to reality as possible for investigating the mechanisms of inhaled particle deposition in the respiratory tract of human and experimental animals. In vitro studies were carried out on the physically-constructed model of the tracheobronchial tree using monodisperse, radio-labeled particles with a geometric diameter of less than 0.1 µm. A unified theoretical deposition model has been developed, which emphasizing the similarities and differences of deposition patterns in various species. Development of the deposition model was based on physical and mathematical models, inhalation experiments, aerosol physical properties, and anatomical and dynamic measurements [47]. Morphometric measurements have been conducted based on silicone rubber replica casts of the respiratory airways of human, Beagle dogs, rats, and Syrian hamsters. The lungs that were used for constructing the casts were maintained within the thorax to keep the exact orientation of the conducting airways. A detailed description of the used in situ method is provided in a paper published by Phalen et al. (1973) [92]. Light and scanning electron-microscopic evaluation and bronchograms were used for validation of the casts. The dimensions of the casts, including diameters, lengthes and bifurcation angles of the airways, were measured from stereo-radiograms using a stereo-bronchographic method, a detail description about the method is provided by Yeh et al. (1975) [174]. It was discovered that during the casting procedure, the bifurcation angles were changed by less than 5%, whereas this discrepancy was 15% for the diameters of major bronchi. By providing the best estimation of the described parameters in the idealized model of airway branching, morohometric measurements were conducted using an abstract of an idealized model. In this idealized model, both parent and daughter branches are tubular segments which are described by parameters like length (L), diameter (d), angle to the direction of gravity (ψ), and angular change in direction associated with each daughter (θ). 3.4. Image-based airway models

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Due to the recent advancement in medical imaging technology, reconstruction of anatomical specimens based on the detailed images of the internal structure of the human body have been possible. The development of such three-dimensional computerized specimens provided an opportunity to build solid replicas for in vitro experiments. Medical imaging modalities can be classified into two categories: • Anatomical modalities: This approach reveals internal structure of the organs which comprises X-ray, computed tomography (CT) scans, magnetic resonance imaging (MRI), ultrasound, etc [175].

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• Functional modalities: Functional modalities or physiological imaging provides information about metabolism, blood flow, etc. which include positron emission tomography (PET), functional MRI (fMRI), electro encephalography (EEG) and magneto encephalography (MEG) [175]. For further investigation on the development of image-based airway models, the focus will be on anatomical modalities for the rest of the section, specially CT and MRI imaging.

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3.4.1. CT-based airway models The very beginning of computed tomographic (CT) imaging refers to the mathematical theory of Radon transform by Johann Radon (1917) ([176, 177]). However, the invention of the first commercially CT scanner was not until 1967 by Sir Godfrey Hounsfield who utilized ”Algebraic Reconstruction Technique (ART)” as the image reconstruction mechanism [178]. Developments in CT technology led to introduction of ACTA (Automatic Computerized Transverse Axial) scanner by Robert Ledley at Georgetown University which was able to scan and produce image from any part of the body; although, these days there are advanced CT scanners with the ability to produce high-resolution images in less than 1 second. In 2007, a project supported by National Institutes of Health/National Library of Medicine (NIH/NLM) entitled ”Visible Human Project” provided a high resolution axial CT scan data for both males and females ([179, 180]). The Visible Human Male CT data was consisted of images with 512×512 resolutions at 1 mm intervals over the length. The female CT data set was more detailed which was comprised of images 15

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at 0.33 mm intervals over the length. Actually, the beginning of the project dates back to 1986 which was an effort to provide a data set of cross-sectional photographs of the human body [181]. The first outputs of the project were male and female detailed anatomical images with a resolution of 2048 × 1216 pixels which were released in 1994 and 1995, respectively. This valuable set of anatomical images have provided information which is used by more than 1000 licensees [179]. Based on these high-resolution anatomical images of the Visible Human data, preliminary work on development and fabrication of detailed hollow airway models was undertaken by Clinkenbeard et al. (2002) [179]. A commercial three-dimensional cloud point airway model based on the NIH/NLM Visible Male anatomical images have been utilized for construction of the hollow airway replica. Selective laser sintering (SLS) rapid prototyping technique was used for fabrication purposes which provided support for all elements during the construction and removing the requirement for further supporting structures. Due to the requirement for firm and laboratory friendly physical model, a polyamide powder with particle distribution size ranged from 15 to 90 µm was chosen for construction of the replica. The accuracy tests for evaluating the precision of the computer model and SLS technique showed that the maximum discrepancies for both were ± 0.1 mm. The ultimate airway replica was durable, slightly flexible, abrasion resistant and undeformable which was consisted of at least five and in several locations six generations with 1-2 mm diameter. Figure 9 shows the airway replica by Clinkenbeard et al. (2002), manufactured by SLS rapid prototyping technique.

Figure 9: The tracheobronchial airway replica by Clinkenbeard et al. (2002) based on the anatomical images of the NIH/NLM Visible Human data [179]. Reprinted by permission of the publisher (Taylor and Francis Ltd, http://www.tandfonline.com).

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Lizal et al. (2012, [151]), carried out a major investigation on development of comprehensive airway models based on the reference model by Schmidt et al. (2004), [158]). Five different realistic and semi-realistic airway geometries have been manufactured with and without oral cavity for optical and deposition measurements. The first two geometries were without the oral cavity and were based on the CT scan data of an adult Caucasian male volunteer in the mid-pharynx region up to trachea, as well as tracheobronchial airway tree based on the model by Schmidt et al. (2004). One of these two manufactured geometries was transparent for optical investigations and the other one was segmented for deposition measurements. The next step was fabrication of two (transparent and segmented) other airway geometries with an oral cavity to investigate the effects of this segment on the airflow structure and particle deposition. The scanned upper part of the Lovelace Respiratory Research Institute wax model (model A) (2005, [182]) was utilized to develop the new models. The last step was designing a simplified, tube-like model with preserved branches volume and angle for Phase Doppler anemometry (PDA) measurements. Tracheobronchial airways of the transparent geometries were restricted to the first four bifurcations; however, segmented geometries were constructed up to seven bifurcation. Due to the requirement for high optical quality in the transparent airway geometries, transparent silicone was 16

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used to create a thin wall around the soluble core of the developed models for construction of the hollow airway casts. The manufactured airway geometries were completely transparent which were consisted of thin walls with 2 mm thickness at the entrance and 1 mm at the outlets. For regional deposition measurements, the airway model should be detachable and there is no need for optical transparency; therefore, the segmented hollow airway geometries were manufactured by stereolithography. Several different investigations have been conducted based on these realistic and semi-realistic airway geometries, which will be presented as follow. Jedelsky et al. (2012) utilized the silicone airway cast without the oral cavity to study the turbulent particle transport by Phase Doppler Particle Analyser (P/DPA) [183]. Steady and cyclic sinusoidal breathing regimes with flow rates of 15, 30, and 60 (l/min) were used to suction the di-2-ethl hexyl sebacate (DEHS) monodispersed particles downstream of the airway cast. Using the realistic segmented airway geometry including the oral cavity (Figure 10 7 ), Lizal et al. (2015) introduced a method based on PET imaging for local deposition measurements [184]. DEHS particles were tagged with fluorine 18 to provide the radioactive aerosol particles for PET deposition measurements. Due to the high spatial resolution in this methodology, possibility of repeating the exact experiments and controlling the boundary conditions were provided. In 2016, Elcner et al. published a paper in which they investigated the flow structures in several cross sections of the realistic transparent airway cast without the oral cavity, using a combination of in vitro experiments and CFD simulations [185]. Sedentary and deep breathing conditions with tidal volumes of 0.5 and 1 L for 4 s inspiration/expiration cycles were used to conduct the simulations and experiments. Good agreement between the experimental and numerical results were observed and highly turbulent and unstable flow fields were reported in the investigated cross sections. Using the segmented airway replica (Figure 10), Nordlund et al. (2017) performed an in vitro experiment to determine regional deposition of monodisperse and multicomponent aerosols [186]. The monodisperse glycerol aerosol and multicomponent liquid solution of electronic cigarettes were employed for experimental investigation and deposited amount of glycerol, propylene glycol and nicotine in the samples were quantified by gas chromatography. Inertial impaction was the dominating deposition mechanism for both monodisperse and multicomponent aerosols and deposition patterns were also similar throughout the airway replica. In order to provide reliable experimental data about regional deposition of glass fibers, Belka et al. (2018) carried out an in vitro experiments using uniform diameter glass fibers and the segmented respiratory airway replica (Figure 10) [187]. Three steady flow rates (15, 30 and 50 l/min) were utilized to introduce the glass fibers to the airway replica which provided the samples for measurement of deposition efficiencies, fractions and densities. The results showed that impaction was the main deposition mechanism. Frederix et al. (2018) utilized an Eulerian internally mixed aerosol model in order to investigate deposition of size-dependent aerosols in a realistic cast of the human upper airways [188]. Sectional discretization of the droplet size distribution function was used to capture size-dependent aerosol dynamics and solve the model. In 2019, Farkas et al. conducted a numerical simulation to track fibers in a complex oro-pharyngeal-laryngeal-bronchial system [189]. Simulations were performed at different inhalation flow rates and two different approaches were utilized for the estimation of drag force. The results were compared to the previous experimental data performed in the same geometry, and a good agreement was observed between the deposition efficiency values. Furthermore, it was revealed that the most satisfactory outcomes were devoted to the simulations which utilized the drag model that considered the anisotropic nature of the geometry of fibers.

7 Reprinted from Journal of Aerosol Science, Vol 117, Miloslav Belka, Frantisek Lizal, Jan Jedelsky, Jakub Elcner, Philip K. Hopke, Miroslav Jicha, Pages 149-163, Copyright (2018), with permission from Elsevier.

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Figure 10: The realistic segmented airway model including the oral cavity. Reprinted from Lizal et al. (2012) [187], with permission from Elsevier.

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In 2019, Ahookhosh et al. conducted an experimental investigation for evaluation of a dry powder inhaler (DPI) and a metered dose inhaler (MDI) using a realistic physical airway model [13]. The airway model was based on a CT data set of a healthy 48-year-old female (1023 contiguous images with 0.5 mm thickness), extended from oral cavity to the fourth generation of the tracheobronchial tree which was fabricated by rapid prototyping techniques. Deposition results were in accordance with the reliable experimental data available in the literature. Deposition fraction was reported in different regions of the model and a comparison was set out between the drug delivery devices in order to elicit the differences, which led to different deposition patterns in the model. 3.4.2. MRI-based airway models The history of magnetic resonance imaging (MRI) refers to the discovery of nuclear magnetic resonance (NMR) by Isidor Rabi (1938) in his studies on molecular beams for measurement of nuclear magnetic moment [190]. In the following years, Paul Lauterbur (1973) successfully described a method to produce the first nuclear MR images and his studies on the applicability of MRI finally led to 2003 noble prize in physiology or medicine. However, the first full-body MRI scanner was not introduced until 1980 by a team led by John Mallard at university of Aberdeen [191]. Over the past decades, magnetic resonance imaging has been a primary tool for morphometric studies, measurement of particle deposition in the respiratory tract and development of oral, nasal and tracheobronchial airway replicas. Guilmette et al. (1989) utilized MR images to study nasal airway dimensions of a non-smoking Caucasian male and results indicated that previous cadaver studies have overestimated the cross-sectional areas of the nasal airways [192]. Swift (1991) developed two accurate nasal replicas based on MR images of an adult and an infant for measurement of nasal aerosol deposition [193]. The results showed that deposition in the child nasal replica was greater than the adult nasal replica in the same flow rate. In 1993, Cheng et al. published a paper in which they described the deposition of radon-220 progeny in four human oral and nasal replicas [194]. This investigation was comprised of two MRI-based and two cadaver-based models which were used to perform the experiments at constant flow rates of 4-20 (l/min). On the basis of the previous morphometric study in 1989, Guilmette and Gagliano (1994) developed a method to fabricate a physical replica based on MR images to investigate the total and regional deposition patterns in the human nasal airways [195]. A series of contiguous MR images with 3 mm-thick slices and 256 × 256 image matrix was obtained from a 53-year-old, non-smoking, Cau18

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casian male. This nasal airway model was one of the first physical MRI-based models which had several advantageous such as accuracy and reproducibility. In 1999, Zwartz and Guilmette developed a new nasal model based on the same MRI data sets that Guilmette et al. (1998) and Guilmette and Gagliano (1994) used, to accurately describe the olfactory region and modify the nasal airway geometry [196]. An aerosol solution consisted of monodisperse dioctyl sebacate particles with fluorescent dye Nile Red for labeling purposes, was utilized to investigate the local particle deposition in the new nasal replica. A Charge Couple Device (CCD) imaging system was used to measure the intensity of fluorescent in different parts of the replica. Using the same nasal replica and imaging technique, Zwartz and Guilmette (2001) investigated spatial deposition patterns by controlling important particle deposition parameters such as airflow rate [197]. The first MRI-based nasal airway replica manufactured by stereolithography refers to Kelly et al. (2004) in their investigation on deposition efficiency of inertial regime particles [53]. Two nasal airway replicas based on the same MR images were produced with different stereolithography machines, in order to study and report the differences of the deposition efficiencies in the replicas with the same MRI source but manufactured with different methods. The results suggested that the differences in deposition efficiencies were related to the surface roughness and airway discontinuities. In 2007, Kimbell et al. carried out a combination of experimental and numerical investigation on nasal spray behaviour using a MRI-based nasal airway model of a healthy adult male [198]. Eighteen different available nasal spray devices were utilized to characterize the sprays, and CFD model of Subramaniam et al. (1998, [199]), was used to conduct a series of simulations at 15 (L/min) inspiratory flow rate. The results showed a good consistency with the previous experimental studies and suggested that spray characteristics, delayed appearance of inspiratory airflow and physical constraints on the release of the particles were the most important factors which affected the performance of the nasal spray devices. In 2013, Zhou et al. conducted a combination of an in vitro experiment and a CFD simulation in the same replica which was developed by Xi et al. (2011), to investigate the deposition of monodisperse oleic acid particles [200]. The anatomically realistic nasal replica was based on the 128 MR images at 1.5 mm intervals over the length. Figure 11 8 illustrates the MRI-based nasal airway model by Xi et al. (2011) [201]. The MRI-based airway models and replicas which were utilized in airflow and deposition investigations, were not only devoted to nasal region, but also to oral and tracheobronchial regions. McRobbie et al. (2003) carried out an investigation to develop a process of MR image acquisition to produce an oropharyngeal physical cast [202]. Eight MRI data sets were provided using two different acquisition strategies [Fast Low Angle Shot (FLASH) and Fast Imaging Steady-state Precession(FISP)] to study the intra-subject, inter-session variability of the MR acquisition techniques.

8 Reprinted

from Journal of Aerosol Science, Vol 42, Jinxiang Xi, Xiuhua Si, Jong Won Kim, Ariel Berlinski, Simulation of airflow and aerosol deposition in the nasal cavity of a 5-year-old child, Pages 156-173, Copright (2011), ith permission from Elsevier.

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Figure 11: The MRI-based nasal airway model by Xi et al. (2011). Reprinted from Xi et al. [201], with permission from Elsevier.

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Corcoran et al. (2003) evaluated four different methods for increasing drug delivery into the MRIbased airway model using helium-oxygen and nebulizer reservoirs [203]. The MRI data set with 3 mm intervals over the length was related to a 5-year-old boy that the mouth, throat, and upper airways down to the carina were included. In 2004, Heenan et al. published a paper in which they described the relationship between the flow field and regional deposition using two different MRI-based extrathoracic airway geometries [204]. The difference between the utilized extrathoracic geometries was referred to the position of the tongue during the data acquisition. The first model included a small oral cavity due to the forward position of the tongue; and in contrast, the second one was comprised of large mouth cavity with the reduced size of the nasopharynx. Both models were manufactured by a rapid prototyper using ABS plastic with 6 mm thickness shell. In a study which was set out to investigate the intersubject and intrasubject deposition measurements, Grgic et al. (2004) utilized seven mouth-throat geometries based on MRI scans [205]. The selected airway geometries were chosen from a large set of MRI-based airway models to be representative of the key mouth-throat dimensions. Some of the airway models were even the mixed of male and female subjects with different ages and nationalities. All seven geometries were fabricated by a rapid prototyper with ABS plastic. In 2008, Minocchieri et al. manufactured a premature infant upper airway replica based on MRI scan in order to investigate the effects of anatomical and physiological parameters on the pulmonary drug delivery in preterm newborns [206]. The MRI-based replica was fabricated by a rapid prototyping machine using a photopolymer (FullCure 720) material and accuracy of the constructed airway replica was studied by a high resolution CT scan which indicated 0.94% relative deviation for airway volumes. The morphometric study on rat respiratory airways by Oakes et al. (2012), led to the first general set of in situ data of Wistar rat lung based on MRI scan [207]. The MRI data set was comprised of four male Wistar rat MR images with 0.2 × 0.2 × 0.27 mm resolution which was utilized to develop a model with 16 airway generations. Airway dimensions were measured for the first four airway generations which showed good agreement with the previous morphometric studies. For further investigation on image-based airway replicas, a review is provided by Lizal et al. (2018) which investigates experimental methods for aerosol deposition measurements in human airways which can be quite helpful [208]. This study provide a detailed overview of experimental techniques that can be utilized for validation of numerical investigations, which can be a guideline for choosing the appropriate respiratory airway models and replicas for experimental studies.

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4. Numerical and mathematical models

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4.1. Idealized respiratory airway models In 1967, Horsfield and Cumming investigated the relationship between radius and volume of the conducting airways of the human lung mathematically to obtain minimal resistance to gas flow [129]. To accomplish this goal, they proposed a method for calculating the angles of branching which led to minimal volume in the conducting airways. Also, a relationship between radius of the parent and daughter branches has been presented which was able to produce minimal resistance in the model. Schum and Yeh (1980) published a paper in which they proposed a computational model to predict deposition of particulate pollutants in several species of mammals [209]. The mathematical model was based on the anatomical model of Weibel, which was consisted of a series of parallel, semi-rigid cylindrical tubes in the bifurcating tree. The predicted deposition data showed a good consistency with the available data in the literature. The results also indicated that particle size, density, and breathing patterns can be considered as critical parameters of regional deposition. In 1993, Balashazy and Hofmann carried out a numerical investigation on particle deposition patterns in two bifurcation geometries (narrow and wide central zone) for several realistic air flow fields [135]. The three-dimensional model was based on the general case of an asymmetric bifurcation which was consisted of four geometrical elements: parent branch, two daughter branches and a central bifurcation zone. The parent and daughter branches were described by cylindrical tubes with individual lengths, diameters, and branching angles which formed the central transition zone. Simulations on the model were conducted under the simultaneous effects such as inertial impaction, gravitational settling, Brownian diffusion and interception to calculate the air flow field. Spatial deposition patterns including hot spots at carinal ridges throughout the bifurcation airways were studied for inspiratory flow conditions. Preliminary work on anatomically modelling of the conducting airways was undertaken by Tawhai et al. (2000), where in a three-dimensional tree-growing mathematical algorithm was implemented to generate a host-shape dependent conducting airway model [210]. This tree-growing three-dimensional algorithm was based on a two-dimensional tree generation Monte Carlo method that has been described by Wang et al. (1992, [211]). The produced model was a computational mesh which showed a good consistency with the reliable morphometric data available in the literature on critical parameters such as branching and length ratios, path lengths, numbers of branches, and branching angles. Branch angles were laid exclusively within the range of ideal angles provided by Horsfield and Cumming [129]. The computational mesh proposed by Tawhai et al. provided a necessary asymmetry which was required for gas mixing, aerosol deposition, and water/heat transfer investigations. In 2002, Calay and co-workers utilized a three-dimensional asymmetric model of the central respiratory airway to investigate the unsteady inspiratory airflow dynamics through a human lung [143]. The implemented single bifurcation model was based on the morphometric data provided by Horsfield et al. (1971, [154]), which was consisted of trachea and two main right and left bronchi and each one was described by straight circular cross-section tube. The angles that right and left main bronchi branched off their parent were 35◦ and 73◦ , respectively. It was found that the utilized single asymmetric bifurcation model is able to provide a number of quantitative and qualitative data which were in accordance with the experimental and numerical investigations in the literature. Shi et al. (2004), performed a numerical investigation on transport and deposition of ultrafine particles in five idealized models [147]. The implemented models were consisted of a single straight pipe, a 90◦ bend, a planar airway model representing G3 to G5 of Weibel’s lung model, a non-planar three generation airway model, and a modified version of the Third model. A comparison between the deposition results of the non-planar and planar airway models showed just small differences. In characterization of pulmonary architecture, Lee et al. proposed a flexible mathematical model of an asymmetric bronchial airway bifurcation (2008, [212]). In this mathematical model, bifurcation structure was determined by 11 independent geometric parameters such as: radius of parent airway, radius of daughter branches, lengths of straight section of daughter airways, etc. Several explicit functions were utilized to describe the shape of the carina where the three airways merge, and also to include parameters such as the blunt shape of the carina as a function of bifurcation asymmetry. A validation study was carried out based on a CT data set of a Sprague Dawley rat lung cast, where a comparison was set out and a good accuracy as conducted between the results of the mathematical model and the CT data set. 4.2. Stochastic lung models As described in section 3.3, deterministic lung models are based on morphometric studies on individual lung casts and parameters defined in these models such as diameter, length, and angles are pre-specified 21

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linear airway dimensions [213]. Furthermore, there are several limitations involved with presented morphometrical data in the literature and a comprehensive anatomical set of data comprised of the entire human respiratory airways is not available [65]. Significant differences have been perceived in results of the experimental deposition studies using the morphomertic models (see [214, 215, 216, 217]) and they were not able to reflect the anatomical complexities of the lung which led to inter-subject variabilities. The first attempt to take the inter-subject variabilities of airway dimensions into account in a statistical manner was made by Soong et al. (1979, [218]), who used Weibel geometry to calculate the functional residual capacity (FRC, refer to subsection 2.2) of the lung ([219, 213]). Using the same geometry, they extended the technique to the acinar region [220]. In these studies, airway dimensions were described by log-normal probability density functions [219]. In the following years, several investigators studied inter-subject variabilities in total and regional deposition using different geometries (see [221, 222, 223]). Yu and Diu (1982) suggested a statistical approach including two random scaling factors to comprise inter-subject variations of the airway dimensions using ”Model-A” by Weibel [224]. However, the great advancement was achieved in the pioneering work by Koblinger and Hofmann (1985) which was the beginning of the stochastic lung models [219]. The proposed stochastic multiple-path model was a Monte Carlo method to describe the asymmetry and randomness of the human respiratory airway system based on the bronchial morphometric data by Raabe et al. (1976, [47]) and pulmonary acinus data by Haefeli-Bleuer and Weibel (1988, [51]) [170]. A statistical lung structure with a random selection of airway branches and as well as particle transport pathways were developed using this technique which allowed for variation in dimensions (diameters, lengths, branching and gravity angles) [225]. In this modeling approach, statistical density functions were used to describe the airway dimensions which led to a geometry that was able to characterize the inter-subject variations of the human lung [65]. In the developed Monte Carlo method, the deposition of the particles was not the aim of the simulation, but the reduction of the statistical weight of the particles in the selected airway was the measurement criteria ([213, 226]). Table 3 provides the airway parameters of the typical path model of Yeh and Schum (1980, [49]), which is based on the morphometric measurements by Raabe et al. (1976). The Monte Carlo method by Koblinger and Hofmann (1985) was also formed based on the same foundation [73]. The presented parameters in the Table 3 such as generation number, number of airways, airway segment diameter, airway segment length, branching angle, gravity angle, cross-sectional area, volume and cumulative volume are showed with n, N , D, L, θ, ϕ, S, V and ΣV , respectively [73]. In 1988, Koblinger and Hofmann also developed a new Monte Carlo program, RALMO, for calculation of aerosol deposition in rat lungs using morphometric data of Lovelace Inhalation Toxicology Research Institute (ITRI) [227]. The results revealed considerable differences in dimensions of major and minor daughters bifurcated from the same parent. The next investigation of Koblinger and Hofmann (1990) on stochastic lung models was a Monte Carlo code, IDEAL-2, for calculation of aerosol deposition in human lungs based on the morphometric data of the bronchial tree by Raabe et al. (1976) and acinar region by Haefeli-Bleuer and Weibel (1988) [213]. The primary characteristic of the developed code was a simulation of random walks of the inhaled particles; but, the results illustrated remarkable differences in deposition distribution throughout the lung between developed Monte Carlo code and deterministic method, that the reasons of the differences were quite unclear [225]. To present a more thorough stochastic model, Hofmann and Koblinger (1992, [228]) developed their Mote Carlo code to scale the number of bronchial airway generations by scaling factors just like diameters and lengths in the previous investigations. Due to the differences in deposition pattern for oral and nasal breathing, two different sets of equations for the nose and extrathoracic region were used [Yu et al. (1981, [229]) and Stahlhofen et al. (1989, [230]), respectively] to supply the model. The results were compared with the experimental data by Heyder et al. (1986, [231]) and considerable differences in total and regional deposition revealed even under controlled breathing conditions. Another Monte Carlo method was developed by Hofmann, Bergmann and Menache (1998) which was based on the upper bronchial airway dimensions by Menache (1997, [232]), with the lower and alveolar airway structure based on the stochastic model [233]. In 1995, Anjilvel and asgharian expanded the single-path model by Schum and Yeh (1980, [209]) based on actual anatomic data, and represented the first multiple-path model of the rat lung [234]. This new model provides a method for calculation of deposition in every airway of the lung model.

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Table 3. Airway parameters of the typical path model by Yeh and Schum (1980, [49]), [73]. n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

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N 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131,072 262,144 524,288 104,8576 209,7152 419,4304 838,8608 3×108

D(cm) 2.01 1.56 1.13 0.827 0.651 0.574 0.435 0.373 0.322 0.257 0.198 0.156 0.118 0.092 0.073 0.060 0.054 0.050 0.047 0.045 0.044 0.044 0.043 0.043 0.030

L(cm) 10 4.36 1.78 0.965 0.995 1.01 0.890 0.962 0.867 0.667 0.556 0.446 0.359 0.275 0.212 0.168 0.134 0.120 0.092 0.080 0.070 0.063 0.057 0.053 0.025

θ(deg.) 0 33 34 22 20 18 19 22 28 22 33 34 37 39 39 51 45 45 45 45 45 45 45 45 45

ϕ(deg.) 0 20 31 43 39 39 40 36 39 45 43 45 45 60 60 60 60 60 60 60 60 60 60 60 60

S(cm2 ) 3.17 3.82 4.01 4.30 5.33 8.28 9.51 13.9 20.85 26.56 31.53 39.14 44.79 54.46 68.57 92.65 150.09 257.36 454.81 833.84 1594.39 3188.78 6090.97 12,181.95 -

V(cm2 ) 31.73 16.67 7.14 4.15 5.30 8.36 8.47 13.46 18.07 17.72 17.53 17.46 16.08 14.98 14.54 15.57 20.11 30.88 41.84 66.71 111.61 200.89 374.19 645.64 3871.80

ΣV(cm3 ) 31.73 48.40 55.54 59.69 64.98 73.35 81.81 95.27 113.3 131.06 148.6 166.05 182.1 197.1 211.6 227.2 247.3 278.2 320.04 386.7 498.3 699.2 1046.4 1692 5563.8

Furthermore, in this model branching pattern was highly asymmetric which was an effective feature in deposition distribution; therefore, it was a more realistic approach for use compared to the single-path models. Hofmann et al. (2000) carried out an investigation on particle deposition in the bronchial and acinar airways of two different morphometric model of the rat lung to specify the differences between multiple-path lung model (MPL) by Anjilvel and Asgharian (1995, [234]) and stochastic lung model (SL) by Koblinger et al. (1995, [235]). They used similar deposition equations in both models so as to relate possible differences in particle deposition to the lung morphologies. Considerable variability in particle deposition among different acini have been observed and variances of acinar deposition in the MPL model was much smaller than those for SL model [236]. For further exploration of the potential of stochastic lung models for prediction of particle deposition, Hofmann, Asgharian and Winkler-Heil (2002) used two different morphometric models of the human lung for modeling intersubject variability [170]. The first one was the stochastic lung model by Koblinger and Hofmann (1985,1990), and the second one was stochastic multiple-path lung model (SMPL) by Asgharian, Hofmann and Bergmann (2001, [237]), which was consisted of 10 SMPL models derived from stochastic lung model by Yeh and Schum (1980, [49]). The results indicated that the structural and volumetric differences of lung morphologies were the main reasons of the intersubject variability in total and regional deposition [170]. Stochastic models have been used not only for simulation of particle deposition but also for modeling of particle clearance in human bronchial airways [238]. In this work, Hofmann and Sturm (2004) utilized Monte Carlo methods for modeling the clearance process of insoluble particles in the bronchial airways for both slow and fast clearance mechanisms. To recognize the best modeling assumptions, particle retention patterns resulted from the developed stochastic model were compared to the available experimental data and a good agreement was observed. The results also suggested that slow clearance mechanisms were the most effective in small airways. In 2007, the deposition model by Asgharian et al. (2001, [237]) was developed by Asgharian and Price for any lung geometry and ultrafine particles [239]. The calculations were performed in many asymmetric bronchial airway models to provide a range of deposition data for ultrafine particles and good agreement was observed compared to the measurements in the literature. 23

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To study the flow field conditions and transportation of inhaled aerosols from the fourth bifurcation to the terminal bronchioles, in 2010 for the first time an individual path model was used by Tian et al. [240]. The developed geometry was consisted of the elliptical Mouth-Throat (MT) geometry (oral cavity, pharynx and larynx) by Xi and Longest (2007, [241]), upper tracheobronchial (TB) airways up to fourth bifurcation based on the anatomical cast dimensioned by Yeh and Schum (1980, [49]), and conducting airways up to 16 generation produced by individual path model by Heistracher and Hofmann (1995, [242]). Figure 12 illustrates the mentioned airway geometry by Tian et al. (2010). The objective of this study was to investigate the transport of inhaled particles using a new proposed respiratory drug delivery approach which called enhanced condensational growth (ECG). Saturated or subsaturated airflow with water vapor was used to deliver the submicrometer or nanometer aerosols to the respiratory system. The results illustrated that utilizing ECG approach led to minor aerosol deposition in the MT and TB regions and targeting the region in the tracheobronchial tree was also possible by controlling the inlet temperature conditions and initial aerosol size.

Figure 12: The respiratory airway geometry by Tian et al. (2010, [240]), including the mouth-throat region and conducting airways up to terminal bronchioles. Reprinted by permission from Springer Nature: Springer Nature, ANNALS OF BIOMEDICAL ENGINEERING, Characterization of Respiratory Drug Delivery with Enhanced Condensational Growth using an Individual Path Model of the Entire Tracheobronchial Airways, Geng Tian, Philip Worth Longest, Guoguang Su et al., COPYRIGHT (2010).

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Tian et al. (2011) published another paper in which they investigated the effects of transient vs. steady state conditions on the deposition of inhaled pharmaceutical aerosol in the MT and TB regions [243]. A new stochastic individual path (SIP) approach was used for modeling the process. Three SIP geometries were produced and in each one after the fourth bifurcation, just one branch of each bifurcation was continued to the terminal bronchioles. The validation study was carried out using concurrent experimental 24

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investigation in MT-TB model and good agreement was observed. This SIP approach in stochastic models helps remove unnecessary computational efforts by a factor of 3 × 105 . In 2012, Longest et al. have used a similar SIP approach to study the deposition of metered dose inhaler (MDI) and dry powder inhaler (DPI) aerosols using different inhalation profiles [67]. Meanwhile, an in vitro experiment was performed using MDI inhaler in the hollow airway replica up to third bifurcation (B3) to validate the CFD simulations and good agreement was reported between the experimental and the CFD data. The MT region of the airway geometry was developed based on the oral airway cast by Cheng et al. (1997, [244]) and CT-scan images of the pharynx and larynx. The upper tracheobronchial airways were based on the anatomical cast by Yeh and Schum (1980, [49]). The presented results indicated that MDI delivered more drug to the tracheobronchial region and less to the mouth-throat region compared to DPI. In an investigation on aerosol deposition in respiratory airways of chronic obstructive pulmonary disease(COPD) patients, Farkas et al. (2019) carried out a simulations using a stochastic airway deposition model [245]. In this deposition investigation, stochastic lung model (SLM) developed by Koblinger and Hofmann (1990, [213]) has been utilized to predict the deposition pattern of a dry powder inhaler (DPI) aerosols in upper airways of the respiratory tract. The results demonstrated that the amount of deposited drug in the respiratory airway is correlated with the degree of disease severity. 4.3. Image-based airway models

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4.3.1. CT-based airway models In 2002, Sauret et al. carried out an investigation on topology of respiratory airways using two different sets of CT images [246]. The first set was devoted to a human tracheobronchial tree cast with 1-mm-thick adjacent slices and the second one was related to a healthy 27-year-old male volunteer. In this study, the geometric properties of the tracheobronchial tree such as diameter, length, gravity, coronal and sagittal angles were studied using a semiautomated computer-based algorithm which was developed by Sauret et al. (1999, [247]). A year later, Sera et al. (2003) reported a two-step method for modeling small airways of the tracheobronchial tree by staining the lung tissue with a radiopaque solution and afterward scanning the lung with a micro-CT scanner [248]. In another study, Schmidt et al. (2004) using high-resolution computed tomography (HRCT) imaging developed a digital reference model of the bronchial airways for further improvements in particle transport and deposition studies [158]. The data set was consisted of CT images with a pixel dimension of 0.35 × 0.35 mm2 and 0.4 mm intervals over the length which was referred to an adult male rubber cast free from pathological problems. The segmentation process of the HRCT images was carried out using a threshold-based algorithm. Two different models were provided for simulation purposes; the first one was a surface representation of the segmented volume and the second one was a graph representation of the branching airways. The graph was a simplified, tube-like version of the surface representation model. A thinning algorithm was implemented for skeletonizing the tubular structure in order to derive the graph presentation. Figure 13 9 illustrates both surface and graph representations of the model developed by Schmidt et al. (2004). Also in 2004, Tawhai et al. published a paper in which they described the development of two MDCT-based (multidetector row X-ray-CT) models of the human and ovine bronchial tree consisted of 10 and 23 generations, respectively [159]. A volume-filling algorithm was used to extend the models throughout the conducting airway system and the results showed good accuracy compared to previous anatomic studies. The study of the airflow structure dependency on mouth-oropharynx-larynx geometry was carried out by Lin et al. (2007) using a realistic MDCT-based model which was comprised of the upper respiratory tract, trachea and tracheobronchial tree up to six generations [249]. The developed model refers to MDCT images with 0.6 mm slice width of a non-smoker, normal, 20-year-old female subject. The comparison of the results with and without extrathoracic region showed that simple inlet boundary condition does not demonstrate the effects of the upper respiratory tract. Figure 14 10 shows the MDCT-based airway model by Lin et al. (2007) [249].

9 Reprinted from Computerized Medical Imaging and Graphics, Vol 28, Andreas Schmidt, Stephan Zidowitz, Andres Kriete, Thorsten Denhard, Stefan Krass, Heinz-Otto Peitgen, A digital reference model of the human bronchial tree, Pages 203-211, Copyright (2004), with permission from Elsevier. 10 Reprinted from Respiratory Physiology & Neurobiology, Vol 157, Ching-Long Lin, Merryn H. Tawhai, Geoffrey McLennan, Eric A., Characteristics of the turbulent laryngeal jet and its effect on airflow in the human intra-thoracic airways, Pages 295-309 Copyright (2007), with permission from Elsevier.

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Figure 13: The tracheobronchial airway models by Schmidt et al. (2004): a) surface representation of the segmented volume data of the bronchial tree b) simplified, a tube-like graph representation of the bronchial tree. Reprinted from Schmidt et al. [158], with permission from Elsevier.

Figure 14: The MDCT-based airway model by Lin et al. (2007), including mouthpiece, upper respiratory tract, trachea and bronchial tree up to 6 generations. Reprinted from Lin et al. [249], with permission from Elsevier.

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In 2010, De Backer et al. conducted a computational fluid dynamic study for validation of the combined single photon emission computed tomography (SPECT), computed tomography (CT) results and demonstrated the importance of correct boundary conditions in numerical simulations [250]. In order to develop a realistic airway model, six adult patients (three men with mean age of 46 years and three women with mean age of 51 years) with mild or moderate asthma underwent two low-dose CT examinations, which resulted in reconstruction of a three-dimensional airway structure comprised of extrathoracic and tracheobronchial tree up to generations with 1-2 mm diameter. CFD simulations showed a good agreement with the results extracted from SPECT/CT examinations which suggest that the results from simulations with appropriate boundary conditions can be as reliable as the results from functional imaging tools. Several other numerical investigations have been conducted on different subjects of pulmonary drug delivery using CT-based airway models that can be referred to for more investigation on CT-based airway models (see [46, 11, 38, 39]). 4.3.2. MRI-based airway models Most of the introduced MRI-based airway models so far were referred to the modeling of the nasal cavity; however, there have been also MRI-based tracheobronchial airway models in the literature which will be introduced in this section. Shi et al. (2007) carried out a numerical investigation on the modeling of inertia particle transport and deposition in human nasal cavities [251]. The implemented model was based on a MRI data set of a healthy, 53-year-old, non-smoking male, which was consisted of two approximately equal size cavities (fossa). The results indicated that most of the deposition occurred in the nasal valve region (anterior part of the human nasal cavity). Ma and Lutchen (2008), conducted a CFD simulation for studying aerosol deposition in the human large-medium airway, in which they developed a MRI-CTbased model extended from mouth (nasal cavity was not included) to the generation 10 with 22 outlets for the right lung and 19 outlets for the left lung [252]. The trachea was included cartilaginous rings and outlet diameters were in the range of 1.8 to 4.4 mm. The upper airway of the model was based on a MRI imaging on a healthy human male; whereas, the large-medium conducting airways were referred to a MDCT data set of a separate healthy human male. Under steady oral inhalation, simulations were performed and a deposition was calculated throughout the model which showed a good consistency with the in vivo and in vitro experiments. The deposition results in the tracheobronchial airways indicated that deposition in this region is dominated by the large-medium airways for the micrometer-sized particles. Xi and Longest (2008) in order to investigate the sub-micrometer aerosol deposition pattern in the nasal cavity developed a model based on the MRI scan of a healthy, nonsmoking 53-year-old male subject [253]. The nasal airway model was consisted of narrow, convoluted, and multi-layer channels with two relatively symmetric passages which were separated by the nasal septum. The particle sizes ranged from 1 to 1000 nm which were inhaled with 4-30 L/min inspiratory flow rates. The simulations were performed using a novel drift flux approach with near-wall velocity correction (DF-VC). The results demonstrated that the implemented particle transport model can provide an effective approach for prediction of sub-micrometer aerosol deposition in the human nasal airways. As can be seen, most of the deposition investigations have focused on adult subjects and since extrapolation of adult’s deposition data to children were not satisfying due to the differences in ventilation rate and scale of the airways, conducting deposition studies on pediatric models seemed necessary. A recent airflow and aerosol deposition study by Xi et al. (2011) in a MRI-based nasal-laryngeal airway model of a 5-year-old boy revealed that in the same inhalation flow rate, children received much more inhaled aerosol in the nasal airways compared to adults [201]. The results were in accordance with the pervious experimental data obtained from nasal airway casts of children, and also in comparison with adult’s data, significant differences in breathing resistance and deposition patterns were observed. The importance of the dimension and morphometry of nasal airway in the filtering efficiency and deposition of inhaled aerosols in this region was also revealed. In order to study the effects of surface texture, Schroeter et al. (2011) reconstructed a series of MRI-based nasal CFD models and replicas with different levels of surface smoothness [254]. Steady-state flow rate and Lagrangian particle tracking were utilized to simulate the particle deposition in the nasal CFD models. In comparison to the experimental data, the results demonstrated that even slight geometric differences have significant effects on deposition patterns in the human nasal cavity. For further investigation on image-based airway models, a review is provided by Koullapis et al. (2018) which investigates computational approaches for aerosol deposition measurements in the human airways [255]. This study provide a detailed overview of computational Fluid-Particle Dynamics (CFPD), which is comprised of a wide range of regional deposition data in human airway models. 27

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A comparison of airway diameters between geometries of the introduced models in the previous sections is provided in Table 4. Six different models were chosen as representatives of the introduced modeling approaches. The first geometry is the symmetric model proposed by Weibel (1963, model-A), which refers to an adult human lung with total air volume of 4800 mL [41]. In this model, regular features of the human branching airways are emphasized and the airway branches multiply toward peripheri by 1 a regular dichotomy. The average diameters of the airways reduce by a factor of 2 3 (see section 3.3.1). The next geometry refers to the asymmetrical airway model by Horsfield et al. (1971), which was based on a resin cast of a normal human conducting airways down to branches of 0.7 mm diameter [154]. The proposed mathematical model was an effort to taken the asymmetry of the bronchial tree into account and for this aim, each lobe was considered separately. The third geometry is devoted to the typical path model by Yeh and Schum (1980, [49]), which is based on the morphometric measurements by Raabe et al. (1976, [47]). The aim of this study was to develop a modeling approach which could be applied to different mammalian species, which led to two models of the human bronchial airways. Table 3 provides a wide range of dimensions referred to this typical path model (see section 3.3.2). The fourth model is the Zhou and Cheng’s airway replica (2005), which was comprised of oral cavity, pharynx, larynx, trachea, and tracheobronchial tree up to fourth generation. The airway replica was based on a silicone rubber cast which was made from an adult cadaver [182]. The next model is a realistic airway replica developed by Lizal et al. (2012), extended from extrathoracic region up to 7th bronchial generation [151]. Lizal’s airway model was based on the airway model by schmidt et al. (2004, [158]), which was derived from a CT data set of an adult man (see sections 3.4.1 and 4.3.1). The last diameters refer to the CT-based airway replica by Ahookhosh et al. (2019, [13]), that was related to a 48-year-old healthy female (see section 3.4.1). It should be noted that the diameters of the first and third columns are mean diameters and in each airway generation, the left and right diameters are equal. As can be seen, despite the differences in the modeling approaches, Table 4 shows a good agreement between diameters of the presented models, except for the Yeh and Schum’s model (third column). This column shows an over-prediction compared to the other columns for all the airway generations. The first two columns are devoted to the idealized models by Weibel (Model-A, 1963) and Horsfield et al.(1971), which both of them are based on morphometric studies on resin casts. Clearly, a good agreement is observed between the diameters of these two models in each airway generation. Similarly, airway diameters of the last two columns are agree well with each other too, because both of the models by Lizal et al. and Ahookhosh et al. are CT-based airway geometries and share the same modeling approach. It is also worth to notice that due to the presence of the heart in the left side of the chest and sharing space with the left lungs, left airways are narrower and longer compared to right airways. As can be seen in Table 4, diameters of the right airway generations are larger than diameters of the left generations. Table 5 shows a comparison of airway lengths for four of the introduced airway models. Just like diameters, a similar agreement is observed between the airway lengths of the CT-based models. However, there are differences between the numbers of the first two columns and the last two columns due to the different modeling approaches.

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Weibel (Model-A) [41] 18 12.2 8.3 5.6 4.5 3.5 12.2 8.3 5.6 4.5 3.5

Horsfield et al. [154] 16 12 8 5.5 11.1 8.9 6.4 4.4 -

Yeh and Schum [49] 20.1 15.6 11.3 8.2 6.5 5.7 15.6 11.3 8.2 6.5 5.7

Generation no. Trachea (G0) G1 G2 G3 G4 G5

Weibel (Model-A, 1963)[41] 120 47.6 19 7.6 12.7 10.7

Yeh and Schum (1980) [49] 100 43.6 17.8 9.6 9.9 10.1

Table 5. Comparison of mean airway lengths (mm) for four different models.

Generation no. Trachea (G0) Left G1 Left G2 Left G3 Left G4 Left G5 Right G1 Right G2 Right G3 Right G4 Right G5

Table 4. Comparison of airway diameters (mm) for six different models. Ahookhosh et al. [13] 14.1 9.9 5.7 5.5 3.7 12.5 9.9 6.1 4.8 -

Ahookhosh et al. (2019) [13] 112.8 24.2 15.4 10.8 -

Lizal et al. [256] 16.3 10.2 6.5 5.6 3.8 2.8 12.6 8.3 5.9 4.4 3.9

Lizal et al. (2012) [256] 27.5 15.5 10.5 -

Zhou and Cheng [182] 15.8 7.1 6 5.9 12.3 7.8 6.5 5.6 -

6. Summary and Conclusion

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Pulmonary route is an ideal pathway to deliver aerosolized drug particles into the lung both in systematic and site targeting ways to treat or prevent respiratory system diseases. To accomplish a successful pulmonary drug delivery, understanding the principles of aerosol deposition and lung physiology seems necessary. Anatomical and physiological factors such as lung morphometry, breathing patterns, fluid dynamics, and particle properties are the most important parameters that should be considered in any drug delivery investigation. The respiratory airway structure is one of these parameters which greatly influence the deposition pattern of inhaled particles. Experimental investigations of aerosol deposition on human subjects and laboratory animals include many difficulties and also there have been legal and public pressures worldwide for finding an appropriate alternative for performing the scientific experiments, therefore developing respiratory airway models and replicas is an important research area for scientists for conducting in vitro experiments, as well as CFD simulations . Casting techniques were one of the earliest choices for providing anatomical airway models for morphometric studies and teaching purposes, which dates back to 14 century in the pre-corrosion casting era. However, most of the replicated living specimens were devoted to corrosion casting era in which a solidifiable medium with a low melting point was utilized to form the replica. In 18th and 19th centuries, several major morphometric studies were conducted using cadavers or airway casts to provide reliable and comprehensive anatomical data sets which led to introduction of the first idealized airway model by Weibel (1963). The earliest idealized models were just a simple and symmetric description of the branching airways which included several primary limitations. In order to resolve these limitations, asymmetrical airway models were introduced which were a more realistic description of the tracheobronchial airway but they were still not good enough to reflect the anatomical complexities of the respiratory tract. In 1980s, studies on inter-subject variabilities led to introduction of stochastic lung models which were statistical lung structures based on Monte Carlo methods with a random selection of airway branches. These statistical lung models were able to describe the asymmetry and randomness of the respiratory airway system which enables them to characterize the inter-subject variations of the human lung. Thanks to the advancement in imaging technology, next generation of airway models were based on CT and MR images which provided an opportunity to develop more realistic models of conducting airways with asymmetric branching patterns. The image-based models were good choices for both manufacturing airway replicas for in vitro investigations and also producing geometries for CFD studies. The presented historical review showed the signs of progress which have been made over the past decades in the development of respiratory airway models. Each model was introduced in detail based on its historical trend, and the strengths, deficiencies and differences of the models with each other were also discussed which can be very helpful for those who are interested in this research area. Moreover, this paper can provide a wide range of reliable references in respiratory tract anatomy and physiology, lung morphometric studies and pulmonary drug delivery. References

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