Soft tissues influence nasal airflow in diapsids: Implications for dinosaurs

The nasal passage performs multiple functions in amniotes, including olfaction and thermoregulation. These functions would have been present in extinct animals as well. However, fossils preserve only low‐resolution versions of the nasal passage due to loss of soft‐tissue structures after death. To test the effects of these lower resolution models on interpretations of nasal physiology, we performed a broadly comparative analysis of the nasal passages in extant diapsid representatives, e.g., alligator, turkey, ostrich, iguana, and a monitor lizard. Using computational fluid dynamics, we simulated airflow through 3D reconstructed models of the different nasal passages and compared these soft‐tissue‐bounded results to similar analyses of the same airways under the lower‐resolution limits imposed by fossilization. Airflow patterns in these bony‐bounded airways were more homogeneous and slower flowing than those of their soft‐tissue counterparts. These data indicate that bony‐bounded airway reconstructions of extinct animal nasal passages are far too conservative and place overly restrictive physiological limitations on extinct species. In spite of the diverse array of nasal passage shapes, distinct similarities in airflow were observed, including consistent areas of nasal passage constriction such as the junction of the olfactory region and main airway. These nasal constrictions can reasonably be inferred to have been present in extinct taxa such as dinosaurs.


| INTRODUCTION
Nasal passages serve a variety of vital functions in extant amniotes. The nasal passage, trachea, and primary bronchi form the air-conducting portion of the respiratory system, delivering air from the environment to the lungs (Kierszenbaum, 2007). Epithelial mucosa in the nasal passages provide a vital protective role against airborne pathogens (Harkema et al., 2006;Morgan et al., 1990). Convolutions of the wellvascularized mucosa function to condition the respired air, modifying the heat and water content of each breath and reducing respiratory evaporative water loss (Jackson & Schmidt-Nielsen, 1964;Schmidt-Nielsen et al., 1970). Airborne odorant molecules are selectively captured along specific regions of the nasal passages, where they initiate odor discrimination pathways in the brain.
Nasal passages and their associated sinuses can also function as resonators, influencing the timbre of exhaled air and providing a primary or secondary role in communication (Brackenbury, 1982;Frey et al., 2007;Nowicki, 1987;Roberts, 1973).
All of these functions were likely present in extinct species such as dinosaurs. Evidence of extensive nasal cavity expansion in a variety of dinosaur lineages suggests that one or more of these functions were targets of selection in dinosaur evolution (Bourke et al., 2018;Evans et al., 2009;Miyashita et al., 2011;Weishampel, 1981;Witmer & Ridgely, 2008). Discriminating between these functions and their importance for dinosaurs requires a deeper understanding of the nasal anatomy within the group. Unfortunately, preservation biases limit our knowledge of dinosaur nasal passages to the bony, outer boundaries of the cartilaginous nasal capsule ( Figure 1). Previous attempts at restoring dinosaur nasal anatomy have relied extensively on these outer boundaries coupled with their placement next to other inferred soft tissues such as the paranasal sinuses (Witmer & Ridgely, 2008). These reconstructions revealed the hard outer limits of the nasal capsule, but the inner boundaries where the physiologically relevant mucosa reside remain unknown. This not only limits our ability to reconstruct what these structures looked like in life, but it also obscures our understanding of the functional potential of this anatomical system. Similar limitations have been found in the articular cartilages of the joints in dinosaurs where extensive soft-tissue involvement greatly affects the functional anatomy of the joints (Holliday et al., 2010;Tsai & Holliday, 2015).
Soft tissues limit the functional range of motion in the limbs (e.g., Hutson & Hutson, 2012), indicating that the full range of motion of extinct animal limbs may be exaggerated. Although not as mobile, nasal passage reconstructions suffer from a similar lack of resolution in extinct animals. Many aspects of the nasal passage are comprised solely of soft tissues, such as the cartilaginous conchae of birds (Bang, 1971;Danner et al., 2017), the muscular hydrostats of elephant trunks (Marchant & Shoshani, 2007;Miall & Greenwood, 1878), and the elaborate nostrils of many bat species (Brokaw and Smotherman, 2020;Usui et al., 2022). These aspects of extinct animal anatomy and physiology are often lost to the vagaries of fossilization, wherein bones, teeth, and other hard parts are often all that remains.
Determining where these inner boundaries reside in extinct species requires a detailed understanding of nasal capsule morphology and physiology in extant animals. As Dinosauria is deeply nested within the more inclusive clade, Diapsida (Benton, 2005;Nesbitt, 2011;Brusatte, 2012) a better understanding of nasal physiology in extant diapsids would greatly add to reconstructions of dinosaur nasal anatomy and associated physiology.
However, a broader comparative survey of airflow dynamics in diapsids has yet to be performed.
This study describes airflow dynamics within the nasal passages of several extant representatives of the diverse clade Diapsida. We used gross dissection and computed tomography (CT)-based, 3D segmentation to visualize and describe the anatomy of the nasal passages. Airflow dynamics are analyzed using computational fluid dynamics (CFD) on a single representative specimen for each species F I G U R E 1 Comparisons of soft-tissue (a) and bony-bounded (b) nasal passages in an axial cross-section of a generalized diapsid nasal cavity. Much of the geometry of the nasal passage is formed from soft-tissue structures that rarely fossilize. Even mineralized structures such as nasal turbinates, may be lost in fossilization due to their fragile construction. cap = cartilaginous nasal capsule, co = concha, max = maxilla, mu = mucosa, nas = nasal, ns = nasal septum, turb = nasal turbinate, v = vomer. studied. We used CFD for airflow analysis as this engineering approach offers the ability to simulate fluid flow in a digital environment, allowing for nondestructive and noninvasive methods of testing delicate and hard-to-access regions of anatomy.
To understand how soft tissues affect the respired air field we first simulated airflow movement in nasal passages that retained their soft tissues (the "true" nasal passage shape). We then digitally ablated all of the soft-tissue boundaries inside the nasal passage, leaving only a bony-bounded (BB) airway behind. These bony-bounded airways represent the typical degree of nasal passage preservation encountered with fossils. We performed a second CFD analysis on these bony-bounded nasal passages and contrasted airflow patterns here with their soft-tissue counterparts.

| Anatomical terminology
Following our previous work (Bourke et al., 2014(Bourke et al., , 2018, we divided the nasal passage into a series of nested layers ( Figure 1).
Bony nasal cavity-The outermost border of the bony nasal passage and everything within it.
Bony and fleshy nostril-The bony nostril (apertura nasi ossea; Baumel and Witmer, 1993;Waibl et al., 2012) is the rostral opening of the bony nasal cavity, bounded by the premaxilla, nasal, and maxilla. The fleshy nostril (naris; Witmer, 2001) is bounded within the confines of the bony nasal aperture, often at the rostral terminus.
Bony and fleshy choana-The bony choana (fenestra exochoanalis; Bellairs, 1949;Jarvik, 1942) is bordered laterally by the maxilla, rostrally by the maxilla and vomer, medially by the vomer and palatines, and caudally by the palatines or pterygoids (crocodylians; Witmer, 1995a). The fleshy choana (fenestra endochoanalis; Bellairs, 1949;Jarvik, 1942) is the "true" choana as it represents the soft-tissue-bounded opening of the nasal passages into the throat. For the sake of clarity, we refer to the fleshy choana simply as the choana, and the bony choana as the fenestra exochoanalis throughout the rest of this study.
Nasal capsule-The cartilaginous structure deep to the bony nasal cavity that serves as the main point of attachment or outgrowth for most of the soft tissues inside the nasal passage (e.g., turbinates, mucosa, conchae).
Conchae and turbinates-Following our previous methodology (Bourke et al., 2014;see also Nickel et al., 1986;Witmer et al., 1999), we separate turbinates from conchae. Turbinates are the cartilaginous or bony outgrowths of the nasal capsule that project into the nasal cavity. Conchae comprise the overlying mucosa covering the turbinates.
Mucosal layer-Various epithelial types and corresponding submucosal neurovascular bundles are found here. Three basic epithelial types can be distinguished in the nasal passage, in roughly rostral to caudal order: variably cornified stratified squamous epithelium, ciliated columnar (respiratory) epithelium, and olfactory epithelium (identified by the presence of olfactory receptor neurons and Bowman's glands).
Airway-The deepest space within the nasal passage where respired air travels.
Despite a multitude of different anatomical arrangements, diapsid nasal passages adhere to the same gross anatomical structure as other amniotes. The nasal passage, or nasal capsule, may be divided into three compartments: Nasal vestibule (vestibulum nasi)-This is the rostral-most portion of the nasal capsule just deep to the fleshy nostril. It may take on a tubular shape and is typically smaller in diameter than the cavum nasi proprium (CNP). The nasal vestibule terminates at the duct for the nasal gland and is usually coated in stratified squamous epithelium. Conchae are variably present within the nasal vestibule.
Cavum nasi proprium-This is the nasal cavity proper or main nasal cavity and is the middle compartment of the nasal passage. The CNP is more capacious than the nasal vestibule as it houses most of the nasal conchae. Both respiratory and olfactory epithelium are found in the CNP, with the latter having a more restricted distribution along the nasal cavity. Olfactory epithelium is most often found in an "olfactory region" of the CNP that is variably removed from the main airflow. This region may further develop into a cul-de-sac known as the olfactory recess (Eiting, Smith & Perot, & Dumont, 2014;Smith et al., 2015). The olfactory recess completely separates olfactory airflow from respiratory airflow during expiration, promoting unidirectional airflow across the olfactory epithelium and increasing odorant molecule sensitivity. Olfactory recesses are associated with macrosmia in mammals (Craven et al., 2010;Eiting, Smith & Perot, & Dumont, 2014).
Nasopharyngeal duct (ductus nasopharyngeus)-Following the terminology of Parsons (1970), we define the nasopharyngeal duct as any connection from the CNP that leads to the choana. This compartment varies in its length and complexity across species and is coated in respiratory epithelium.

| Study species
All specimens, with the exception of data contributed by C. G. Farmer and E. R. Schachner, are housed in a public repository, the Ohio University Vertebrate Collections (OUVC). Specimen condition varied depending on acquisition. Alligators, ostriches, and turkeys had only their heads preserved, requiring mass estimates based on regression equations taken from the literature (Coulson et al., 1973 for alligators;Hinds & Calder, 1971 for birds). Squamates were often preserved in total and were directly weighed. All OUVC specimens were postmortem cadaveric salvage specimens ethically donated from legal sources (e.g., governmental agencies, wildlife rehabilitation facilities), and the animals' deaths were independent of this project, the authors here, or Ohio University. Specimens are legally housed in the OUVC under the terms of permit #14-2762 issued by the Ohio Division of Wildlife.
Crocodylians: Various specimens of American alligator (Alligator mississippiensis, N = 4) were examined with CT and/or dissection. The specimen used for CFD modeling was OUVC 10389, a yearling male American alligator approximately 468 g in mass. The specimen was acquired as a salvage specimen from the Rockefeller Wildlife Refuge (Louisiana Department of Wildlife and Fisheries). This specimen was chosen for the clarity of its nasal passages and the detailed scan resolution (92 µm).
Birds: Multiple specimens of wild turkey (Meleagris gallapovo, N = 3) and farmed ostrich (Struthio camelus, N = 10) were examined with CT and/or dissection. Specimens used for CFD modeling were OUVC 10636, a subadult ostrich of approximately 74 kg in mass, and OUVC 10599, an adult wild turkey approximately 4.9 kg in mass. The heads of the turkeys were obtained from local hunters as part of a legal controlled hunt and donated to the OUVC, whereas the ostriches were obtained as salvage specimens from a commercial processing center (Nutri-Tech, LLC, Beaver City, Nebraska).
Squamates: Multiple specimens of green iguana (Iguana iguana, N = 3) and savannah monitor (Varanus exanthematicus, N = 3) were examined with CT and/or dissection. Specimens used for CFD modeling were OUVC 10603 (Morphosource 000S19937), a juvenile green iguana with a mass of 870 g, obtained from the Miami Metro Zoo in Miami, Florida, as a salvage specimen generated by the zoo's feral pest eradication program. The monitor specimen used for CFD modeling was OUVC 10675, a young adult male, 1.73 kg in mass, whose body was donated to our study following a previous, unrelated study (McElroy & Reilly, 2009). CT data used for comparison in this study were contributed by C. G. Farmer and E. R. Schachner, based on live animal data acquired from an unrelated study (Schachner et al., 2013).

| Dissections
The nasal capsules of squamates, birds, and crocodylians were dissected to directly observe the anatomical relationships of the structures within the nasal cavity. Dissections were either performed on whole specimens or on heads that were hemisected, allowing access through the medial wall (cartilaginous septum) of the nasal capsule. In certain instances, the nasal capsule was physically excised from the nasal cavity by removal of surrounding bone to better observe anatomical relationships within the capsule.

| Computed tomography
The heads of juvenile alligators, turkeys, iguanas, and monitor lizards were scanned at the Ohio University's MicroCT Scanning Facility (OuμCT). Specimens were scanned with a General Electric eXplore Locus MicroCT scanner. Scanning parameters were 60 kV at 450 μA with an isotropic voxel size of 45 or 90 μm. Data were exported in DICOM format for segmentation in Avizo 6.3-7.1 (VSG, Thermo-Fisher Scientific). Ostrich and large alligator heads were scanned using a Toshiba Aquilion 64 slice CT scanner at OhioHealth O'Bleness Hospital in Athens, Ohio at a slice thickness of 300 μm.

| Model reconstruction
DICOM data were read in Avizo 6.3-7.1. The left airway of each specimen was segmented using Avizo's segmentation tools. The single exception was the savannah monitor, which preserved a better right airway than left. The presence of a complete nasal septum in all the species studied obviated the need to model both nasal passages as the septum maintained complete separation of airflow through to the choana. Each nasal capsule was segmented into two models. The first model included the soft tissue encompassing each airway, creating a cast of the airway in the nasal capsule that showed all the places that the air field could travel. The second model removed most soft-tissue boundaries, creating a bony-bounded nasal cavity more in line with fossil preservation. Some soft-tissue boundaries were retained, as they could be reliably inferred from osteological correlates (e.g., paranasal sinuses; Figure 2).
Segmented models were transferred to Geomagic Studios 10 (3D Systems Geomagic, Rock Hill, SC) where they were cleaned of scanning and segmentation artifacts (e.g., polygonal spikes and islands). Cleaned models were reimported into Avizo for volumetric model testing and boundary labeling. Models were assigned a series of boundary conditions that would induce physiologically realistic airflow (i.e., pressure-driven flow from nostril to choana during inspiration and the reverse for expiration). Three boundary conditions were placed on the model (Figure 3b). These boundaries were: (1) a pressure inlet located at either the naris or choana for inspiration and expiration, respectively; (2) a pressure outlet located at either the choana or naris for inspiration and expiration; and (3) an impermeable wall boundary condition assigned to the rest of the nasal capsule.
After cleaning and boundary labeling, models were converted into tetrahedral meshes for fluid dynamic analysis. To ensure that our results were mesh independent, we created multiple grid resolutions ( Figure 3c) and performed a grid refinement study (see Section 2.5).

| Physiological parameters
We simulated resting respiration for all four models. To best approximate physiological relevance, we surveyed the literature to obtain viable volumetric flow rates for resting respiration in each species (Table 1). Respiration data for squamates is limited. Despite numerous studies looking at factorial scope, blood pH, and other aspects of metabolism in squamates, we only found a single published study that attempted to survey respiratory variables in this group (Bennett, 1973). Further complicating matters were the lack of data on the nonventilatory period (NVP) for the animals being studied.
Most reptiles and amphibians exhibit diphasic breathing in which air F I G U R E 2 Example of airway segmentation using a wild turkey (Meleagris gallopavo, OUVC 10599). Heads are CT scanned (inset) and these data are used to segment out the airway based on either its soft-tissue (a) or bony boundaries (b) CT, computed tomography.
F I G U R E 3 Example of workflow using (a) the skull of an American alligator (Alligator mississippiensis, OUVC 10389). Segmented airways were assigned a series of boundary conditions (b) before tetrahedral conversion. Three different model resolutions (c), coarse (321 thousand elements), intermediate (766 thousand elements), and fine (1.8 million elements), were modeled to test for grid independence. is first expired then inspired and held within the lungs for a variable length of time (Milsom, 1988(Milsom, , 1991. Mechanical analyses suggest that diphasic breathing evolved as an adaptation to minimize the costs of ventilation in animals whose metabolic demands did not require continuous breathing to satisfy oxygen requirements (Milsom, 1984;Vitalis & Milsom, 1986). The nonventilatory period varies between species, individuals, and even individual breathing bouts, making documentation of NVP durations extremely important for a variety of physiological variables such as metabolic rate (Thompson & Withers, 1997). For this study, NVP knowledge was necessary for calculating inspiratory drive ( = tidal volume/inspiration time). Without this knowledge, calculations of volumetric flow rate would be exceedingly low, producing results that do not accurately reflect the shape of the air field during resting respiration. To account for NVP, we adjusted our estimates of breathing frequency from the literature by incorporating an 80% NVP. This proportion was based on previous recorded NVP values in reptiles (Frappell et al., 2002;Milsom, 1984;Thompson & Withers, 1997;Vitalis & Milsom, 1986).
Whereas this proportion would likely change depending on the animal and the situation in which it was measured, incorporating an 80% NVP into data taken from the literature served to reduce respiratory cycle time down to 1-2 s/breath; resulting in "burst" breathing rates that fell in line with literature values on reptiles that had incorporated this apnoeic period (Milsom, 1988;Vitalis & Milsom, 1986).

| Computational fluid dynamic analysis
Fluid dynamic analysis was performed using the CFD package, Fluent 13 (ANSYS Inc.). CFD set up and analysis followed previously outlined methods (Bourke & Witmer, 2016;Bourke et al., 2014;Bourke et al., 2018). In brief, we used a 3-dimensional, doubleprecision pressure-based solver. We performed a cross-sectional analysis of the airway to calculate the estimated Reynolds and Womersley numbers for the air field. We used the equation from Holmes et al. (2011) to calculate the Reynolds number based on flow rate: where Q = the volumetric flow rate measured in m 3 /s, P = the wetted perimeter in meters (Foss, 1998), and v = the kinematic viscosity of air (1.6036e −5 m 2 /s at 30°C).
We performed a cross sectional analysis of the nasal passages by obtaining the Reynolds numbers for airway cross sections taken roughly every 3 mm along a path paralleling the respired air field.
Wetted perimeter and area measurements were taken directly using the built-in tools in Avizo 6.3-7.1. Reynolds calculations indicated that laminar flow should be present for our three reptile species and our turkey (Table 2), whereas the potential for some transitional flow existed in the nasal capsule of the ostrich model (Table 2).
Flow steadiness was determined based on calculations of the Womersley number (Wo; Womersley, 1955;Loudon & Tordesillas, 1998), as defined for the respiratory system (Craven et al., 2009) in the following equation: T A B L E 1 Masses and estimated resting respiration rates for specimens used in this study.  Coulson et al. (1973).
e Direct measurement.
f Scaled from Giordano and Jackson (1973), and incorporation of an estimated 80% NVP; g Scaled from Hopkins et al. (1995) and incorporation of an estimated 80% NVP. where f = the frequency of oscillation (Hz), and Dh is the hydraulic diameter of the airway. Womersley numbers were calculated on the same cross sections used to obtain the Reynolds number. Results indicated that a quasi-steady flow should be present for all of our species (Table 2).
For most specimens, we applied the standard laminar viscosity model for continuity and momentum: where u u x y z → = → ( , , ) = the velocity vector and ρ = the density of air.
The ostrich model incorporated Wilcox's two equation κ-ω turbulence model with the addition of a shear stress transport (Menter 1994) as this more robust approach has been found to perform best with dynamic flows within the nasal capsule (Craven et al., 2009;Liu et al., 2007) and better capture the transition zone from laminar to turbulent flow (Chen et al., 2009). Standard sea-level atmospheric pressure (101,325 Pa) was used for the area surrounding the nostrils.
Volumetric flow rate for each specimen was converted into a mass flow and used to determine the pressure gradient within the nasal passage via the "target-mass-flow-rate" option in Fluent. Pressure and velocity coupling were calculated via the SIMPLEC algorithm along with a nodebased discretization gradient. We used a second order accurate spatial discretization scheme for pressure, momentum and (when applicable) turbulence. Models were allowed to run until the solutions had reached a normalized residual of error at or below 1.0 × 10 −4 (Bourke et al., 2014). Point surface monitors placed at various locations on the models were employed as a secondary means of determining convergence independent of continuity and momentum. Converged results were analyzed using Fluent 13 and Avizo Wind 7.1. Models were tested during resting inspiration and expiration.
To ensure that results remained mesh-independent, a three-grid convergence index (GCI) for each model was calculated using a grid refinement ratio of 2 (i.e., the coarsest model was half the resolution of the intermediate model which was half the resolution of the finest model; Figure 3). GCI calculations followed the methods of Roache

| Grid independence
We used the area weighted average for pressure drop at the choana as our convergence variable of interest. Grid independence was verified for our finest resolution airways, with GCI results indicating errors of less than 10% for most models (Table 3). As expected, soft-tissue airways required more tetrahedral elements than bony-bounded airways to accurately reflect the geometry of the nasal capsule.

| Nasal vestibule
In Alligator, as with all extant crocodylians, the nasal vestibule is a small, J-shaped structure extending ventrally a short distance from the naris before curving caudally to join the CNP ( Figure 4).
In contrast, the nasal vestibule was much larger in both the bird and lizard species examined. In the turkey and ostrich, the nasal vestibule was a spacious structure housing the rostral and atrial (turkey only) nasal conchae ( Figures 5 and 6). These conchae reduced the internal diameter of the airway in this region. In the turkey, the presence of an operculum over much of the bony nasal aperture, along with the atrial concha, served to further reduce the airway dimensions ( Figure 5c). In contrast, the ostrich naris was large, resembling a sports-car air scoop. In both species, the caudal extent of the nasal vestibule was demarcated by a raised ridge, the crista nasalis, separating it from the CNP (Figures 5c and 6c).
The iguana and savannah monitor presented elongate and tubular nasal vestibules ( Figure 7). In the iguana, an expansion of the vestibule was observed deep to the naris ( Figure 7b). This medial expansion of the vestibule has been hypothesized to act as a reservoir for the hypersaline products released by the nasal gland . In the savannah monitor, the nasal vestibule was comprised of a proximal and a distal limb ( Figure 7c,d). The distal limb extended from the caudally placed nostrils, rostral to the tip of the snout where it formed an expanded cupola (Bellairs, 1949). The proximal limb extended caudally from the cupola where the nasal vestibule became rounder in cross section. A berry-shaped spherical expansion of the vestibulum was observed just before the terminus of the nasal vestibule ( Figure 7d). In both T A B L E 3 Grid convergence index results. species, separation of the nasal vestibule from the CNP was distinguished by the presence of a raised mucosal structure-akin to the crista nasalis in birds-referred to as the postvestibular ridge by Parsons (1970; Figure 7b,c).

| Cavum nasi proprium
This portion of the nasal cavity is extensively developed in crocodylians. The rostral expansion of the CNP, along with the presence of the preconcha in this region, mirrored the welldeveloped nasal vestibule in birds and lizards. The CNP continues into a caudodorsal expansion we refer to as the olfactory recess based on its physical separation from the nasopharyngeal duct, and thus the main air field, via the pterygoids ( Figure 4). The concha in Alligator is a semi-scrolled structure residing in the olfactory recess along with another mucosal structure, the postconcha. The medial wall of the postconcha forms the lateral boundary for the air field ( Figure 4).
The CNP of both birds studied here contained the remaining conchae. The middle concha is well developed in both species. Its shape is either scrolled (turkey, Figure 5) or branched (ostrich, Figure 6). The medial aspect of the middle concha leads directly into the caudal concha, which sits caudodorsal to the middle concha. The caudal concha is a hemispherical shape in both species with partial scrolling observed in the caudal concha of the ostrich ( Figure 6).
The CNP of Iguana is a spacious structure that houses a single enlarged concha (Figure 7a,b). In the savannah monitor the CNP is a much more abbreviated structure featuring a rostrocaudally compressed, dorsoventrally elongated concha (Figure 7c,d). This concha curves ventrally towards the nasopharyngeal duct.

| Nasopharyngeal duct
This region is well developed in crocodylians. In Alligator, the nasopharyngeal duct extends caudally from the primary choana to the secondary choana within the enclosed pterygoids ( Figure 4). In the bird and lizard species, the nasopharyngeal duct is variably developed. In both birds, the nasopharyngeal duct starts at either the caudal half (ostrich) or the caudal ¼ th (turkey) of the middle concha. It is a fairly short, wide structure in ostriches, whereas in turkeys the nasopharyngeal duct extends caudally for a distance away from the CNP before reaching the choana ( Figures 5 and 6).
In Iguana, the nasopharyngeal duct is more developed caudally than rostrally. This results in direct access to the choana from the rostral half of the concha whereas the caudal half of the concha remains separated from the choana via a medial shelf ( Figure 7a).
The choana itself is a long, teardrop-shaped structure that runs much of the length of the tooth row. The widest end of the choana is at its caudal terminus. A similar architecture of the nasopharyngeal duct was observed in the savannah monitor ( Figure 7c).
As with Iguana, a medial shelf separates a portion of the concha.
However, given the smaller rostrocaudal dimensions of the CNP in this species, this duct is noticeably smaller than it is in the iguana.
The nasopharyngeal duct arches ventromedially towards the choana. The choana of the savannah monitor is a fairly small, rostrocaudally elongated structure that opens into the oral cavity near the distal-most maxillary teeth.

| Soft-tissue and bony-bounded nasal capsule morphology
Bony-bounded nasal capsules in all species studied were much less defined than were their soft-tissue counterparts (

| Airflow in soft-tissue nasal capsules
For ease of comparison between each species our description of nasal airflow is divided by nasal passage compartment.

| Nasal vestibule
The short length of the nasal vestibule in the alligator meant that inspired air moved quickly through it before jetting into the somewhat more spacious preconchal meatus (Video S1A). Expiration showed the same pattern albeit in reverse.
Vorticity was observed in the nasal vestibule of both squamates and birds, though the cause of the vorticity was different for the two groups. In the avian species, vorticity and flow separation were the result of contact with the rostral and atrial (turkey) nasal conchae.
The initial vortex was invoked by air banking off the rostral concha of both birds (Videos S2A and S3A). Air moved medially around the

| Airflow in bony-bounded nasal capsules
Bony-bounded nasal capsules featured pressure drops and respiratory velocities that were fractions of their soft-tissue counterparts.
The large empty spaces within the nasal capsules produced more

| DISCUSSION
The results of our analysis provide a first ever comparative look at airflow in diapsids. These data offer insights into the broader comparative discussion of nasal anatomy and physiology of vertebrates.

| Laminar airflow is common across species
Despite vast differences in morphology and metabolic physiology, we  Vogel, 1994). Under a laminar flow regime, this resistance further increases in proportion to velocity (Swift, 1982;Vogel, 1994). In contrast, turbulent conditions produce localized pressure drops that greatly increase resistance of the fluid to forward momentum. Instead of increasing in direct proportion to the velocity gradient, turbulent pipe flow increases resistance by the square of velocity (Swift, 1982). Thus, pipes with turbulent flow require an overall steeper pressure gradient to maintain the same flow rate as pipes with laminar flowing fluids (Vogel, 1994). Physiologically, this means that a nasal passage pushing turbulent air through it requires substantially more energy. We found evidence for nasal morphology promoting laminarity in areas where the airway became constricted.
This increases wall contact and associated resistance, promoting laminar flow. Nasal passages dilate in response to high flow resistance, and many species are known to switch to oropharyngeal breathing during moderate to intense exercise (England & Bartlett, 1982;Lafortuna et al., 2003;McCaffrey & Kern, 1979;Saibene et al., 1981). Both of these physiological responses reduce airway resistance, maintaining laminarity of airflow.

| Air field partitioning and olfaction
The partitioning of the air field into multiple channels was observed in all the species studied. Air field partitioning varied between species, with the two birds exhibiting the most subdivided air field. However, for all of our species, there was at least one air channel composed of slower moving air that passed into the animal's olfactory region. We determined the location of the olfactory region based on previous anatomical studies and known epithelial distributions. The only species that did not show a velocity reduction of olfactory air was the turkey.
For the other species, the presence of slower olfactory flow mirrored observations from previous studies in other species (Craven et al., 2009;Negus, 1958;Eiting, Perot, & Dumont, 2015;Pang et al., 2016). Our results indicate that diapsid nasal capsule soft-tissue anatomy functions in creating air field heterogeneity.
In crocodylians, the greatly elongated nasopharyngeal duct is completely separated from the olfactory region via a roofing over by the pterygoids. This sharp sequestration of the olfactory region from the nasopharyngeal duct can be compared to the transverse lamina (lamina transversa) of mammals (Smith et al., 2015). The transverse lamina is considered an early innovation of crown Mammalia. Variation in the location of the transverse lamina determine the size and extent of the olfactory recess (Eiting, Smith & Perot, & Dumont, 2014), with macrosmatic mammals such as dogs and rats showing the most welldeveloped olfactory recess (Craven et al., 2010). A sharp pressure gradient between the olfactory recess and the main pressure drawn at the choana forced air to travel unidirectionally through the recess during inspiration and remain largely stagnant during expiration (Craven et al., 2010). This flow pattern produces an uneven distribution of odorant molecules across the olfactory recess, allowing for the fine separation of odors based on their molecular characteristics, similar to a gas chromatograph (Mozell, 1970;Schoenfeld & Cleland, 2005).
We observed the olfactory recess of the alligator model functioning in the same capacity as the olfactory recess of macrosmatic mammals, indicating that crocodylian nasal anatomy facilitates macrosmia.
Known epithelial distribution and behavioral studies further F I G U R E 15 Oblique rostral view of airflow through the CNP of an ostrich (Struthio camelus, OUVC 10636) during inspiration. Arrows represent gross airflow pattern in that region based on multiple air streamlines. Dotted arrows represent air travel through the middle meatus, obscured by the concha. caud co = caudal concha; cr nas = crista nasalis; mid co = middle concha. CNP, cavum nasi proprium.
Olfactory channel separation was also observed in the ostrich, which separated the caudal concha from the underlying nasopharyngeal duct via the cartilaginous body of the middle concha, forcing olfactory-bound air to access the caudal meatus only from the medial branch of the middle meatus. As with the alligator, little to no airflow was observed in the caudal meatus during expiration, suggesting that ostriches may also have a true olfactory recess, albeit one built strictly from geometry of its cartilaginous conchae. In contrast, the olfactory region of the turkey remained partially patent to the main air field via a caudal communication between the olfactory meatus and the choana. This connection to the choana in the turkey allowed bidirectional flow of air to occur within the olfactory region. This produced a complete changeover of olfactory air during expiration-or olfactory washout-reducing contact time of odorant molecules with the olfactory epithelium. Our results suggest that turkeys have much lower potential to separate and distinguish airborne particles as compared to ostriches. Our interpretation receives some support from field observations of wild turkeys, which readily eat shelled corn placed next to mothballs (Pelham & Dickson, 1992). Similarly, domestic turkeys, unlike other domestic fowl, show no preference for soiled (high ammonia content) or unsoiled substrates when given a choice (Monckton et al., 2020).
We were somewhat surprised to observe airflow separation in the nasal capsule of the squamate species. A hallmark of Squamata is the vast expansion of the vomeronasal system, at the assumed cost of olfactory sensitivity (Schwenk, 1993). Anatomically, the CNP of squamates does not appear to offer an anatomical means of isolating olfactory airflow from respiratory airflow in the form of an olfactory recess like the ones we observed in the alligator and ostrich. For the squamates, we expected to see a more uniform pressure drop across the CNP with air flowing across the entire concha. However, the results of our fluid dynamic analyses revealed heterogeneous flow within the CNP. For iguanas, this separation of airflow occurred over the caudodorsal region of the concha ( Figure 17) and appears to have been afforded by the spiral-shaped cartilage forming the nasopharyngeal duct. This spiral shape created a medial shelf that served to isolate the caudal region of the concha from the choana, resulting in a higher-pressure section of the concha. This separation from the main airway reduced but did not eliminate olfactory washout during expiration (Figure 17c). We observed a similar flow pattern in the savannah monitor, which housed a medial ridge along its concha. This ridge separated airflow from the rostral and caudal aspects of the concha. This airflow regionalization along the concha aligned well with the known distribution of epithelial types on squamate conchae (Gabe & Saint Girons, 1976;Rehorek et al., 2000) and agrees with prior anatomical studies of squamate nasal architecture (Bellairs & Boyd, 1950;Bellairs, 1949;Bernstein, 1999;Kratzing, 1975).
Together, they suggest that previous interpretations of squamate (and reptile) conchae as strictly olfactory in function (Hillenius, 1992;Ruben et al., 1998Ruben et al., , 2012 have oversimplified the physiology of these  (Figures 4-7). The preconchal meatus of crocodylians appears to function aerodynamically as an elongate nasal vestibule, complete with a constriction at its caudal terminus just before the olfactory recess. The result of these airway constrictions was a localized pressure drop that created a jetting effect that pushed air into the more spacious CNP, or (for birds) into the middle meatus. This Venturi effect imparted extra momentum on the airborne particles, pushing them farther into the olfactory regions of the nasal passage. The presence of two counterrotating vortices in the preconchal recess of the alligator (Figure 12b; Video S1B) would have further helped push air into the olfactory recess via viscous entrainment of air particles.

| Potential sinuses in ostrich and monitor lizard
The paranasal sinus system of archosaurs is extensively developed (Witmer & Ridgely, 2008;Witmer, 1995a) with all these sinuses possessing ostia that open directly into the nasal capsule. We did not model these sinuses in our species. The sinuses and their ostia are often located perpendicular to the direction of the respired air field.
These locations, coupled with being dead-end spaces, indicate that most of these sinuses are not well ventilated. The only known exception comes from the antorbital sinus of birds, which can be actively ventilated via compression and expansion of the connected suborbital diverticulum as it interleaves between the jaw muscles (Witmer, 1997). This type of air movement is unique in that is localized to just the antorbital sinus and its associated suborbital diverticulum, with air movement driven by jaw muscles instead of a pressure gradient imposed by the respiratory musculature. Incorporating paranasal sinuses into our models would have added extra complexity with little benefit to airflow resolution. To verify this, we performed an exploratory test involving a model of our yearling alligator airway that incorporated all the available paranasal sinuses in that specimen. Our results confirmed the presence of stagnant air within the multiple sinuses surrounding the nasal capsule ( Figure 25).
An unintentional secondary test occurred in our models of the ostrich and savannah monitor. Both species incorporate structures that appear to function as sinuses, at least under our CFD analysis. In the ostrich, we observed a dorsal extension of the caudal concha that formed an inflated bulla within the skull (Figures 16a and 26a). For the savannah monitor, a potential sinus was observed in a ventral extension off the caudal limb of the nasal vestibule (Figures 7c   and 26b). The bilateral symmetry of these structures in the monitor lizard and ostrich, coupled with their presence in multiple specimens, validated that they were not artifacts of preservation. We observed stagnant airflow in both structures during inhalation (Figure 26), further supporting the position of these structures as sinuses. Some airflow recirculation was observed in the putative sinus of the monitor lizard during exhalation, though velocity of recirculated air remained low. The structure of both sinuses is different between the two species. Witmer and Ridgely (2008) figured the bulla in ostriches as part of the caudal meatus and olfactory recess, largely due its placement near the olfactory bulbs and their associated nerves. Upon dissections, we observed a similar, yellow-colored epithelial covering of the bulla as was seen on the caudal (olfactory) concha, indicating that olfactory epithelium does extend into this region (figured in Bourke et al., 2014). However, the epithelial lining was much thinner within the bulla and the entire bulla structure resided substantially dorsal to the caudal concha where it inflated the overlying frontals and nasals. This hard-tissue pneumatization is a hallmark of the paranasal sinuses in archosaurs and mammals (Witmer, 1995a(Witmer, , 1999, and indicates that the bulla developed as an opportunistic invasion of the surrounding bone from the caudal concha (Witmer, 1997). Bulla formation from a diverticulum of the caudal concha would likely have brought some olfactory epithelium with it based on its origin. The thinner covering of olfactory epithelium in this region coupled with the lack of any appreciable olfactory flow in the bulla suggest a minimal role in olfaction. If the bulla is a sinus then it developed intracapsularly as opposed to the extracapsular origin of paranasal sinuses (Witmer, 1995b(Witmer, , 1997. At this point, it remains possible that the olfactory bulla in ostriches is an extension of the olfactory recess that-under a more ballistic breathing regime such as gular pumping (the sauropsid equivalent of sniffing)-air could cycle through. Further histological investigation and modeling approaches are required to determine the exact function of this structure.
In contrast to the ostrich, the sinus observed in the varanid was a soft-tissue-only evagination of the nasal vestibule. The shape of the sinus resembled the extraconchal recess, a nasal structure previously considered as a potential paranasal sinus in lizards (Bellairs, 1949;Parsons, 1970 [= subconchal recess]; Bellairs & Kamal, 1981;Witmer, 1999). As with the extraconchal recess, the structure that we observed evaginating ventrally from the nasal vestibule was a soft-tissue-only structure with no associated bone pneumatization. In the monitor lizard, these sinuses may be an epiphenomenon caused by an incompletely floored nasal capsule (Bellairs, 1949).

| Soft tissue and bony-bounded nasal passages
Airflow in bony-bounded nasal capsules was markedly different from that of their soft-tissue counterparts. Bony-bounded nasal capsules produced slower moving, more homogeneous air, with airway stagnation being more commonplace in all the species studied.
Surprisingly, respired air in the bony-bounded airways did occasionally show similar, albeit cruder, patterns to their soft-tissue counterparts. In the turkey, iguana, and varanid, the air field in the bonybounded nasal capsule reproduced certain spiral motions of the air field also seen in the soft-tissue nasal capsule (Figures 21a, 23a, 24).
These results indicate that some aspects of the bony outer boundaries are responsible for shaping the respired air field. In these instances, soft tissues act more to augment and refine these characteristics. This phenomenon was best exemplified in the in dinosaurs with well-developed olfactory lobes (Bourke et al., 2014).
With that said, bony-bounded airways are not uninformative. The presence of certain flow patterns in even these "low-resolution" models of nasal anatomy have the potential to illuminate the true airflow patterns in the living animals. Airflow reconstruction in extinct species do benefit from these first pass, low-resolution studies as they can identify regions of airflow that may have been real (Bourke  et al., 2014). In certain cases, extensive calcification of the nasal passages can even serve to highlight the real shape of the nasal passage, barring only slight increases in airway caliber due to mucosa deterioration (Bourke et al., 2018).

| Accounting for missing soft tissue
Comparing airflow patterns between soft-tissue and bony-bounded nasal capsules revealed just how much air field shape is dictated by soft tissues (Figure 28). Our volumetric measurements of the softtissue contribution to the nasal passage found substantial variation between nasal regions across species (Figure 29). From our survey of these regions in each species, a general pattern emerged. The nasal vestibule showed the most variation in soft tissue volume ( Figure 29).
This agrees well with general anatomical studies which found this region of the nasal capsule to be the most structurally labile (Bang & Wenzel, 1985;Stebbins, 1948;Witmer, 1995b). Surprisingly, this pattern held true for the alligator as well despite its rather miniscule nasal vestibule. The large amount of soft tissue filling the space of the alligator nasal vestibule is due to the unique narial musculature of crocodylians (Bellairs and Shute, 1953) coupled with extensive erectile tissue (Porter et al., 2016) that may be further elaborated into visual and auditory structures as in gharials (Martin and Bellairs, 1977). For the squamate species, the bony-bounded nasal capsule did not completely encapsulate the length of the soft-tissue nasal capsule due to soft tissues that extended beyond the border of the bony nasal aperture. These soft-tissue extensions represented a significant proportion of the nasal capsule in the varanid, with over half of the convoluted nasal vestibule extending beyond the borders of the bony nasal aperture (Figure 9).
The CNP proved to be the least variable region for soft-tissue proportions ( Figure 29). Despite vast differences in conchal shape and number between the study species, the proportional volume of soft tissues comprising this region was fairly steady at a mean of 54% savannah monitor-may lack an osseous roof altogether, thus allowing for substantial, unencumbered elaboration of this region of the nose.
An important observation we noted in our comparisons of the bony-bounded and soft-tissue nasal capsules was the remarkable compression of the airway in all the species in our study ( Figure 28).
In the soft-tissue nasal passages of all five specimens, the average distance from the center of the air field to the nearest mucosal wall was less than 2.5 mm, with many areas compressing down to less F I G U R E 27 Pressure map of the bony-bounded airway in the savannah monitor (Varanus exanthematicus, OUVC 10675). Ridge on the septomaxilla acts as a relatively high-pressure zone with a relatively low-pressure tunnel. Arrow represents gross airflow pattern in that region based on multiple air streamlines. than 1.5 mm (Table 4). These small distances agree well with previous comparative nasal studies on mammals (Jackson & Schmidt-Nielsen, 1964;Langman et al., 1979), birds , and lizards . Such remarkably small distances from the air field to the nasal wall can be explained by the process in which heat, moisture, and odorants are transferred throughout the nasal passage. All of these processes are diffusion dependent. More accurately, they are convective-diffusion dependent, as diffusion alone is only effective over very short distances (Vogel, 1994). Convective-diffusion transfer efficiency can be augmented by increasing the surface area of the substrate relative to its volume, and by increasing the residence time of the molecules as they move through the structure (Collins et al., 1971;Schmidt-Nielsen et al., 1970;Vogel, 1994). Anatomically, there appears to be two methods of accomplishing this. One way is to split the nasal passage into multiple, smaller compartments as observed with the various scrolled or branched conchae of birds and mammals. The second method is to maintain a single channel, but compress and F I G U R E 28 Comparison of soft-tissue (yellow) and bony-bounded (gray) airway morphologies across the taxa in our study. Numbers correspond to cross section locations on the skulls. The savannah monitor skull and cross sections were mirrored to align with the other four taxa.
extend the overall length of that channel as observed with the nasal passages of squamates, crocodylians, and some dinosaurs (Bourke et al., 2018).
Even large species, such as the 74 kg ostrich from our study, or the 600 kg giraffes and oxen used by Langman et al. (1979), had radial distances from the center of their air fields to the nearest mucosal wall of approximately 2 mm. This remarkable conservation of nasal passage caliber indicates that the physical limitations of diffusion remain constant even as body size increases. Thus, even large animals should be expected to have extremely narrow nasal passages.
Diversity of nasal passage shape becomes a byproduct of the different ways in which each species solves their common diffusion problem.
Looking at extinct animals such as dinosaurs, airway proportions and the remarkable stability of airway distance within the nasal passages indicates that many previous nasal passage reconstructions in dinosaurs and other extinct species, grossly overestimate airway size ( Figure 30). Such enlarged airways have direct consequences for any analyses that use them to determine aspects of physiology such as olfactory sensitivity (Ostrom, 1962), air conditioning capacity (Bourke et al., 2018;Wheeler, 1978), or even metabolic rate (Ruben et al., 1996).  T A B L E 4 Average radial distance from the center of the air field to the nearest mucosal wall (mm) in the soft-tissue nasal capsules of the study specimens.

| Critique of methods
All data used in this study came from CT scanned specimens. The resolution of these scans varied depending on whether they were hospital-based, "low-resolution" CT scans or higher resolution, µCT scans. This variation in resolution has the potential to introduce artifacts during the segmentation process, especially when discriminating between adhered mucus and the underlying, cartilaginous conchae. These artifacts can adversely affect the geometry of the final segmentation, producing downstream effects that can produce misleading results in the final analysis. Similarly, specimen preparation before CT scanning can affect final interpretations of the scan as some specimens had more mucus-ridden nasal passages than others.
To counter this problem, we only used the cleanest CT scans for our CFD model reconstructions. To reduce mucus infilling of the nasal passages, we prepared each specimen by lightly blowing compressed air through the nasal passages (one nostril at a time) and then rinsing the specimens in water. We relied on our survey of multiple specimens for each species studied. These other specimens were dissected and/or CT scanned as well. The breadth of data for each species modeled provided a necessary cross-check against regions of the nasal passage where even our best scans may have been partially obscured by mucus, allowing for accurate reconstructions of obscured data (e.g., concha curvature). The presence of a fleshy, extensible snood in turkeys posed a potential challenge as this structure would often lie in the way of one side of the nasal passage, obscuring the nostril to varying extents. We physically folded the snood out of the way in instances such as this, maintaining full view of the nasal passage during the scanning process. As our turkey specimens were frozen instead of fixed, the snood retained its lability.
Our use of a yearling alligator as a model for airflow in the species could lead to unrealistic airflow patterns compared to the adult animal as young animals have disproportionate facial features compared to adults (i.e., they are "baby faced"). We chose a yearling alligator as its small size allowed us to perform a high resolution µCT scan of the animal. Further, airway clearance was easier to achieve compared to the much longer airways of adult animals. Adult alligators are rare in most comparative physiology studies as the living animals are difficult to manage. Though our animals were all post mortem, large adults were rare compared to young adults and juveniles. The size of adult alligators limits them to hospital CT scans (600 µm resolution) and the nasal passages are more difficult to remove excess mucus from, resulting in a more limited pool of data. Alleviating some of these concerns, we incorporated two adult animals into our larger comparative survey. A large adult (OUVC 9761, Morphosource: 000S21795; Witmer & Ridgely, 2008) and data from a live, young adult used by Sanders and Farmer (2012). Our survey revealed near identical nasal passage anatomy in both adults and young juveniles with only slight increases in radial distance to the mucosal wall (~0.5-2 mm). For our study, the largest difference between the yearling alligator and adults should be in gross airflow parameters (i.e., larger animals breathe more air in at once). Larger flow rates are offset by having an overall larger nasal passage as long as that nasal passage retains the same geometry. Nasal geometry has been found to provide strong stability to gross air field patterns across a wide range of flow rates (Bourke & Witmer, 2016). As such, the patterns we observed in the yearling should largely reflect patterns seen in the adult animal. We find support for our interpretation in a recent study on nasal airflow in gharials (Bourke et al., 2022).
Both crocodylians share a similar nasal passage arrangement complete with an olfactory recess. Near identical unidirectional airflow patterns were observed in the olfactory recess of gharials, as in our alligator, despite the three orders of magnitude size difference in the animals studied. In crocodylians, the largest anatomical shift to the nasal passage that occurs through ontogeny is the formation of the paranasal sinuses. However, these extra openings lie adjacent to the nasal passage and should have a negligible effect on airflow patterns as shown by our test using the two well-formed paranasal sinuses in our yearling alligator (Figure 25).

F I G U R E 30
Adjusting the bony-bounded nasal passage of the theropod, Majungasaurus crenatissimus (FMNH PR 2100). Insets show anatomical regions where previous Extant Phylogenetic Bracket based inferences are supported by CFD-based inferences for soft tissues. (a) More compressed and terminally placed nostril within the bony nasal aperture (red outline). (b) Soft tissue separating the nasal vestibule from the cavum nasi proprium (e.g., the crista nasalis) are required to jet air into the olfactory region. (c) Olfactory region would have housed an olfactory concha with a shape that varied between a large swelling and a coil. (d) Fleshy choana would have been located at the caudal end of the fenestra exochoanalis. Most of the fenestra would have been covered in mucosa. (e) Adjusting the BB-airway (left) to account for similar airway-mucosa distances as extant animals (right) greatly reduces the volume of the nasal passage in life. Note that the mucosal adjustment shown here does not account for the convolutions imposed by mucosal ridges and/or conchae.
Last, our use of tetrahedral models over hexahedral or hybrid tethex meshes has the potential to miss aspects of airflow that these more advanced models can capture. This difference in resolution can be offset by increasing the number of tetrahedral elements in the model. The meshes used for our analysis were all in excess of 1 million elements with the more complicated airways of the turkey and ostrich in excess of 2 million elements (Table 3). At this size, our models should have the necessary number of nodes and cells to capture the details of resting airflow patterns that we were looking for in our study. For more complicated analyses of heat transfer or wall shear stress (e.g., Bourke et al., 2018Bourke et al., , 2022, hexahedral, polyhedral, or hybrid meshes would be a better choice for capturing the subtle interactions at the fluid-wall boundary.

DATA AVAILABILITY STATEMENT
CT data for the five specimens used in the CFD analysis are openly available on Morphosource.org. Green Iguana (OUVC 10603) can be found at: https://www.morphosource.org/concern/biological_ specimens/000S19937. The rest of the specimens and associated models may be found at: https://www.morphosource.org/projects/ 000536232.

PEER REVIEW
The peer review history for this article is available at https://www.