Computational Fluid Dynamic Modeling Reveals Non-linear Airway Stress During Trachea Development

Normative trachea dimensions and aerodynamic information during development was collected to establish clinical benchmarks, and showed that airway development seems to outpace respiratory demands. Infants and toddlers’ trachea exhibit higher aerodynamic stress that significantly decreases by teenage years. This implies large airway pathology in younger children may have a more substantial clinical impact.

The respiratory tract undergoes significant growth during childhood development, and understanding this growth is of paramount importance in pediatric airway management. In the setting of complex comorbidities, clinical decision-making in complex pediatric airway disorders, in particular laryngotracheal obstruction, can be a challenge. Previously, studies have measured tracheal dimensions (length, anterior-posterior diameter, cross sectional area, shape, etc) in an effort to establish normative data in the pediatric population, reporting that dimensions correlate well with age or weight (1-10). However, such static measurement lacks functional information.

Computational fluid dynamics modeling (CFD) is a method of applying fluid mechanics to create virtual flow models (11-14). Using this method, radiographic images can be imported and extracted to provide objective, reproducible airflow metrics (11,12). Studies have demonstrated that increased tracheal airway CFD metrics, such as wall shear stress and peak flow velocity, have a strong correlation with respiratory symptoms(13,14). Functionally, there is evidence that these metrics may alter epithelial cell morphology, function, and signaling (15-17). Thus, CFD has the potential to enhance not only the clinical decision-making in complex pediatric airway disorders, but can also elucidate the pathophysiologic processes of airway disease(14). Currently, neck computed tomography (CT) and airway endoscopy with Cotton-Myer grading are useful for providing characterization but lack functional data on airflow dynamics. These techniques require either anesthesia or patient cooperation, limiting their application in children. Assessment can be further complicated with complex and multi-level airway pathology. CFD could provide useful functional data in assessing airway stenosis by providing information in addition to traditional assessment of airway geometry. However, a major barrier of the application of CFD in laryngotracheal pathology is that these methods are not validated for clinical use, and normal computational benchmarks of the pediatric trachea have not been established.

Our aim for this study was to obtain normative CFD metric benchmarks of the large airway throughout childhood development. By comparing established data on pediatric airway geometry with our CFD-derived airflow data, we can link novel aerodynamics metrics with airway geometry and clinical symptoms, and the confluence of these elements can enhance future clinical decision making. These novel insights of pediatric tracheal development will provide a framework for future studies examining airway pathology.

Methods

Internal Review Board (IRB) approval was obtained prior to the initiation of this study. A retrospective chart review of the electronic medical record at a tertiary pediatric hospital identified children that received a CT neck or CT chest without airway pathology. ICD-9 and ICD-10 codes were used to identify scans obtained for non-airway related pathology, such as lymphadenitis and benign neck masses. This resulted in a collection of 1625 patients. Images were then reviewed, confirming the capture of the entire laryngotracheal complex. Insufficient images or presence of airway anomalies (tracheal compression, deviation, stenosis, malacia) were excluded. After exclusions, 25 eligible subjects were selected for inclusion into five different age cohorts with 5 subjects per cohort. Age cohorts were categorized as 5 weeks – 12 months (infant), 13 months – 36 months (toddler), 37 months to 6 years (early childhood), 7 years to 12 years (late childhood), and 13 years to 17 years (teenager). For each subject, demographic information (weight, sex, age) was collected.

CFD modeling of the laryngotracheal airway was then performed. All models were created using the same steps and measures, as previously described (14). In brief, images were loaded into AMIRA (Visualization Sciences Group, Hillsboro, OR, USA), a three-dimensional data-visualization software that allowed the geometry of the airway to be extracted and modeled in three dimensions from the cricoid to the carina.

The models were smoothed to remove rough exterior edges and then exported as a Stereolithographic (STL) file prior to uploading into ICEM CFD 16.2 (Ansys, Inc, Canonsburg, PA, USA). Then, the geometry was meshed with 1,000,000 to 3,000,000 tetrahedral elements for further fluid dynamic testing. This mesh was then transferred into ANSYS Fluent 16.2 (Ansys, Inc, Canonsburg, PA, USA), which allowed different fluid dynamic properties to be applied.

The inhaled minute volume (V_E) was calculated individually for each subject using their weight (M) documented on the same day of the CT scan, based on a previously published formula (18):

$$\text{Male (sitting awake):}{\stackrel{.}{V}}_E=(1.36\pm 0.10)M^{0.44\pm 0.02},r=0.996$$

$$\text{Female (sitting awake):}{\stackrel{.}{V}}_E=(1.89\pm 0.40)M^{0.32\pm 0.06},r=0.897$$

The inspiratory air flow through the trachea was simulated using a standard k-omega turbulence model with low-Reynolds corrections. The walls were assumed stationary and no-slip. The convergence, and pressure-velocity coupling were applied using methods previously described and validated through experimental studies (19). Figure 1, A highlights our study protocol.

Figure 1:

Outlines of our study protocol. (A) The geometry of each subject’s airway is extracted from cricoid to carina, modeled in three-dimensions, and processed for computational fluid dynamics modeling (CFD). (B) Examples of CFD simulated flow velocity and wall shear stress (WSS) contour plots (one subject from each age group). In the colorized scale, blue represents lower values and red represents higher values. Visually, both peak flow velocity and WSS gradually decrease as a function of age, but more significant decreases are seen in the 13 to 17 years age group.

The resulted CFD metrics (Figure 1, B and Figure 2) were evaluated with respect to age using Pearson correlations, as well as categorically by age group using generalized linear models with post-hoc analysis. Statistical analyses were conducted in SAS Enterprise Guide and statistical significance was evaluated at P < .05.

Figure 2:

Top row: Linear correlations (Pearson) were found between (A) resistance, (B) average cross-sectional area, (C) trachea length and age. Bottom row: Comparison of (D) resistance, (E) Peak airflow velocity (PFV) and (F) Peak Wall Shear Stress (WSS) between different age groups as well as percent changes between age groups. Group 1: infant 5 weeks–12 months, group 2: toddler 13–36 months, group 3: early childhood 37 months-6 years; group 4: late childhood 7-12 years; and group 5: teenager 13-17 years. For resistance, the differences are significant between all groups, but for PFV and peak WSS, the differences are only significant between late childhood and teenager.

Results

Demographic data of the study subjects is included in Table I (available at www.jpeds.com). Male and female subjects were similarly represented. Age cohorts included a wide range of subject weights per group. All images were successfully modeled. Wall shear stress (WSS, the forces parallel to the wall surface (reported in Pascals)), peak flow velocity (PFV, the maximum velocity of air through the trachea (reported in meters/second)), average cross-sectional area (reported in millimeters²), and resistance (the pressure employed by the airway on incoming air (reported in Pascals/milliliters/second)) were successfully derived from all models (Figure 1, B and Figure 2).

Table 1:

Demographic data including mean age, percent gender, and average weight at time of scan

Age groups	Number of subjects	Age (Mean age, 95% CI)	Sex (%Male, %Female)	Weight at scan (Kg, 95% CI)
5wk - 12mo	5	8mo (5.44-10.56)	40%,60%	9.42kg (6.99-11.85)
13mo - 36mo	5	23mo (15.75-30.25)	40%,60%	12kg (9.7-15)
37mo - 6yr	5	5.2yr (4.47-5.93)	80%,20%	20.76kg (16.48-25.04)
7yr - 12yr	5	9.6yr (8.6-10.6)	40%,60%	28.54kg (23.33-33.75)
13yr - 17yr	5	15.6yr (14.42-16.8)	80%,20%	59.15kg (56.57-61.75)
ALL	25		56%,44%

There was a negative linear correlation between age and airway resistance (r=−0.84, p<0.0001, Figure 2, A), with significant differences between cohorts (Figure 2, D, p<0.05). Similarly, mean cross-sectional area and trachea length also correlated positively with age group (for cross-sectional area r=0.89, p<0.0001, for length, r=0.94, p<0.0001, Figure 2, B and C). However, correlation between age and both PFV and WSS appear to be nonlinear (Figure 2, E and F). Although there was no statistically significant difference between infant, toddler, early childhood, and late childhood groups, there was a significant difference between PFV and WSS of the late childhood and teenage year groups (mean PFV of age 7-12 = 2.89 m/s vs age 13-17 = 1.97 m/s, p<0.05; mean WSS of age 7-12 = 0.19 vs age 13-17 = 0.09, p=0.05, Table II [available at www.jpeds.com]).

Table 2:

Results data with average values for each of the computational fluid dynamics modeling metrics in each age group

Age groups	Flow rate (ml/s+SD)	Cross-sectional area (mm2+SD)	Length (cm+SD)	Resistance (Pa/mL/s+SD)	PFV* (m/s+SD)	WSS† (Pa+SD)
5wks-12mo	60.58 (4.55)	40.18 (5.63)	4.6 (1.1)	0.09 (0.02)	3.38 (0.25)	0.25 (0.06)
13mo-36mo	69.52 (6.58)	52.82 (7.45)	5.5 (0.6)	0.06 (0.01)	3.62 (0.51)	0.24 (0.05)
37mo-6yr	85.38 (7.60)	72.65 (6.73)	6.9 (0.8)	0.05 (0.01)	3.32 (0.45)	0.22 (0.08)
7yr-12yr	94.82 (8.32)	89.44 (19.10)	8.4 (0.8)	0.03 (0.01)	2.89 (0.37)	0.20 (0.03)
13yr-17yr	132.80 (11.03)	191.27 (49.90)	9.9 (0.5)	0.01 (0.003)	1.97 (0.55)	0.10 (0.07)

^*PFV=Peak airflow velocity

^†WSS=Wall Shear Stress

Discussion

CFD modeling has demonstrated utility in multiple clinical and scientific applications. Examples include the assessment of rhinological and laryngotracheal pathology as well as characterizing performance in the rational design of constructs for tracheal replacement (12,14,20,21). By modeling disease entities such as nasal polyps and tracheal stenosis, we are able to identify with precision how airflow is altered in the presence of obstructive disease. Comparison of modeled flow in tracheal stenosis compared with age matched norms revealed drastic increases in wall shear stress, resistance, and peak flow velocity (14). These metrics better correlated with symptoms of respiratory distress compared with radiographic or endoscopic measurements in a pilot study, supporting that CFD could serve as an instrument for functional assessment (22). Modeling the laryngotracheal airway pathology requires an understanding of normal dimensions and normal physiology particularly during growth and development. Establishing normative CFD metrics in the pediatric airway would support more rigorous functional assessments of airway pathology.

Pediatric airways experience rapid change in dimensions during development. The average diameter of the normal infant airway is 5 mm, which increases to 8mm by 10 years of age (23). Continued growth occurs until adulthood, where the adult normal airway has a diameter of 15mm to 20mm (24). Our findings support previous cadaveric studies finding that the pediatric trachea exhibits linear growth from infancy to adolescence (3). When examining the rate of growth, our cohorts mirror the rate seen in endotracheal tube approximation using the Cotton-Myer grading scale, as well as previously studies that show linear correlation between age and cross-sectional area derived from CT (4). Thus, the measurements that we derived from imaging serving as basis for CFD modeling are consistent with changes reported in cadaveric, endoscopic, and radiographic studies of pediatric airway dimensions.

Beyond anatomic changes, there are also dramatic changes in physiologic demand throughout development. Infant oxygen consumption at rest is double that of the adult, 6ml/kg/min in infants versus 3ml/kg/min in adults. Similarly, infant CO2 production is much higher at 100-150ml/kg/min compared with 60ml/kg/min in adults. Children also have lower functional residual capacity and need more frequent ventilation (25). Average respiratory rate decreases continuously throughout development: the normal neonatal respiratory rate is 35-55 breaths/minute, which decreases to 22-30 breaths/minute by one to three years of age. The normal respiratory rate for teens is even lower at 12-20 breaths/minute, mirroring adults. Decreased respiratory rate is associated with larger tidal volumes, which may result in an increase in airflow stress metrics (peak velocity, WSS).

However, our data shows the contrary. As children and their airways grow, there are expected increases in laryngotracheal cross-sectional area as well as decreases in resistance. Matching with previous geometric measurements, airflow stress metrics (WSS, PFV) decrease as a function of age (see the negative correlation in Figure 2, E and F), due to the expansion of airway cross-sectional area. Furthermore, this decrease is not statistically significant across the first four age groups (infant, toddler, early childhood, late childhood) but becomes significant during the transition from late childhood to teenage years (−32% change, p<0.05 for PFV; −52% change, p<0.05 for WSS). This suggests that the airways of infants and children are under the most aerodynamic stress, which then reduces significantly by the teenage years. This seems to hold true for both males and females. Airway development seems to outpace the respiratory demands with a reduction of PFV and WSS despite increasing total respiratory flow rate as a function of age, which implicates that airway pathology in younger age groups may carry more substantial clinical implications.

The mechanism for this paradoxical finding with development as well as its functional impact is unknown. One plausible explanation is that our simulation only focused on the tidal volume during restful breathing, but the dimensions of trachea must also be equipped to handle the whole lung vital capacity during strenuous activity. Functionally, there is preliminary evidence that WSS generated by airflow in the airways may alter epithelial cell morphology, function and signaling (15-17). More work and stratification of variables are needed to better understand the functional impact of this pattern of airflow metrics changes with age.

This study has several limitations. Computing one CFD model requires 10 hours to complete on average. Specialized computer equipment and multiple software programs, as well as knowledge of computer and physics-based engineering are required. These considerations limited us to a certain number of scans for study, which prevented more rigorous assessment. The rigid model of the airway is also a limitation, as fluid structure interaction can potentially modify the airway structure and resultant computational metrics. In addition, several of the metrics, especially in the teen cohort, had relatively large standard deviations that suggest variation between age groups. We believe that these fluctuations are representative of the population but validation studies would be valuable to prove this. Future studies should investigate longitudinal changes of an individual airway with regards to CFD metrics as well as devote more attention to specific age and sex specific differences, effects related to height, comorbidities, genetic syndromes, and ethnicity.

We conclude that the normal pediatric airway undergoes alterations in airflow metrics with age that can be examined with computational fluid dynamics modeling. Wall shear stress, peak flow velocity, and resistance are highest in the infant airway and decrease during development until adulthood. Resistance decreases in a linearly fashion, however both wall shear stress and peak flow velocity remain relatively stable until the teenage years before undergoing significant decline. Defining normative functional airflow benchmarks can help define the clinical implications of laryngotracheal pathology. Computational fluid dynamics modeling may prove to be a useful diagnostic and surgical planning tool for patients with airway pathology, augmenting current diagnostic approaches.

Abbreviation List:

CFD

Computational fluid dynamics

CT

Computed tomography

PFV

Peak airflow velocity

WSS

Wall Shear Stress