Effect of Nasal Airway Nonlinearities on Oscillometric Resistance 2 Measurements in Infants

1 EFFECT OF NASAL AIRWAY NONLINEARITIES ON OSCILLOMETRIC RESISTANCE 2 MEASUREMENTS IN INFANTS

4 B. Radics1, G. Makan2, T. Coppens3, N. André4, C. Page4, L. Dégrugilliers5, S. K. Bayat6, Z. Gingl2, Z. 5 Gyurkovits7, T. M. Tóth8, Z. Hantos9,10*, S. Bayat11,12*

6 1. Department of Pulmonology, University of Szeged, Hungary 7 2. Department of Technical Informatics, University of Szeged, Hungary 8 3. St-Luc University Hospital, Brussels, Belgium 9 4. Department of Otorhinolaryngology, Amiens University Hospital, Amiens, France 10 5. Department of Pediatric Intensive Care, Amiens University Hospital, Amiens, France 11 6. Inria Grenoble, Equipex Amiqual4Home, Grenoble, France 12 7. Department of Obstetrics and Gynaecology, University of Szeged 13 8. Department of Mineralogy, Geochemistry and Petrology, University of Szeged 14 9. County Hospital for Chest Disases, Deszk, Hungary 15 10. Department of Anaesthesiology and Intensive Therapy, Semmelweis University, Budapest, 16 Hungary 17 11. Department of Pulmonology & Physiology, Grenoble University Hospital, Grenoble, France 18 12. Inserm UA7 STROBE Laboratory, Grenoble, France 19 20 *Senior co-authors

21 Running head: Intrabreath oscillometric resistance in nasal airways.

23 Corresponding author:

24 Sam BAYAT MD PhD 25 Dept. of Clinical Physiology, Sleep and Exercise 26 Grenoble University Hospital 27 CS 10217, 38043 Grenoble Cedex 9, France 28

31 Supplemental Material available at:

32 URL: https://github.com/sambayat/Online-Supplement.git

33 DOI: https://doi.org/10.5281/zenodo.3676456

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 34 ABSTRACT

35 Oscillometric measurements of respiratory system resistance (Rrs) in infants are usually made via the

36 nasal pathways, which not only significantly contribute to overall Rrs, but also introduce marked flow 37 (V’)-dependent changes. We employed intrabreath oscillometry in casts of the upper airways

38 constructed from head CT images of 46 infants. We examined oscillometric nasal resistance (Rn) in

39 upper airway casts with no respiratory flow (R0), and the effect of varying V’ on Rn by simulating tidal

40 breathing. A characteristic nonlinear relationship was found between Rn and V’, exhibiting segmental

41 linearity and a prominent breakpoint (V’bp) after log-log transformation. V’bp was linearly related to 2 42 the preceeding value of end-expiratory volume acceleration (V”eE; on average r =0.96, p<0.001). Rn

43 depended on V’, and R at end-expiration (ReE) showed a strong dependence on V”eE in every cast 44 (r2=0.994, p<001) with considerable inter-individual variability. The intercept of the linear regression

45 of ReE vs. V”eE was found to be a close estimate of R0. These findings were utilised in re-analysed Rrs

46 data acquired in vivo in a small group of infants (n=15). Using a graphical method to estimate R0 from

47 ReE, we found a relative contribution of V’-dependent nonlinearity to total resistance of up to 33%. In 48 conclusion, we propose a method for correcting the acceleration-dependent non-linearity error in

49 ReE. This correction can be adapted to estimate R0 from a single intrabreath oscillometric 50 measurement, which would reduce the masking effects of the upper airways on the changes in the 51 intrathoracic resistance.

53 Key words: Forced oscillations; upper airway casts; respiratory mechanics

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 54 NEW & NOTEWORTHY

55 Oscillometric measurements of respiratory system resistance (Rrs) in infants are usually made via the 56 nasal pathways, which not only significantly contribute to overall Rrs, but also introduce marked flow 57 acceleration-dependent distorsions. Here we propose a method for correcting flow acceleration- 58 dependent non-linearity error, based on in vitro measurements in 3D-printed upper airway casts of 59 infants as well as in vivo measurements. This correction can be adapted to estimate Rrs from a single 60 intrabreath oscillometric measurement.

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 61 INTRODUCTION

62 The contribution of nasal airway resistance (Rn) to total respiratory system resistance (Rrs) is a central 63 problem in infant pulmonary function testing, since infants are obligate nasal breathers during the 64 first several months of life. Measurements of lung function in this population are therefore usually 65 performed through a facemask, unlike in older children and adults.

66 The contribution of Rn to that of the Rrs in infants has been studied previously by posterior 67 rhinomanometry. Using this technique, Polgar and Kong (23) estimated this contribution to be 26%, 68 while Stocks and Godfrey (25) found a higher value of 49%. Using low-frequency oscillometry during 69 apneic periods, Hall et al. (8) studied the impedance of the nasal pathways in infants, by measuring 70 nasal pressure with a miniature catheter-tip transducer inserted through a nostril. They found a 45%

71 contribution of the nasal impedance to Rrs.

72 Although some discrepancy in previous estimates of the contribution of Rn to Rrs may be attributed to

73 differences in methodology and population, measurement and interpretation of Rn is profoundly 74 complicated by the anatomical irregularity and complex flow rheology of the nasal passages. The 75 nonlinear pressure (P) -flow (V’) relationship in the upper airways contributes to the dynamic

76 changes in Rrs, which have been well-documented with intra-breath oscillometry in adults (2, 19, 21),

77 children (1) and infants (7). Measurement of Rrs at points of zero V’ (namely at end expiration and

78 end inspiration, ReE and ReI, respectively) minimizes the nonlinear contribution of the nasal pathways 79 and the consequent bias in the estimation of R of the lower respiratory tract. Intra-breath

80 oscillometry is a unique lung function technique that is able to identify these zero-flow values of Rrs.

81 The aim of this study was to use intrabreath oscillometry in anatomically faithful casts of the nasal 82 pathways of infants from birth to 2 years, reconstructed from computed tomography (CT) images.

83 We assessed the lowest oscillatory R without superimposed breathing (R0), as well as the effect of

84 varying V’ on Rn by simulating breathing through the casts. We characterized the relationships of Rn 85 to V’ and volume acceleration (V”). Based on these relationships, we propose a graphical method to

86 correct the error in intrabreath oscillometric Rrs measurements that results from V’-dependent

87 nonlinearities. The relative contribution of these nonlinearities to Rrs was further assessed in a set of 88 intrabreath oscillometric measurements in infants.

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 89 METHODS 90 91 Study population 92 Data of head CT examinations of infants from birth to 24 months, available in the Department of 93 Radiology of the Amiens University Hospital database, performed between October 2011 and August 94 2014, were collected for analysis. Requirement for written informed consent was waived for this 95 retrospective study by the Internal Review Board of the Amiens University Hospital. Cases not 96 including the entire nasal passages from the nares to the tip of the epiglottis, and those with 97 craniofacial abnormalities or upper airway mass based on the radiologist’s report, were excluded. 98 Forty-six image sets met these criteria. Inidcation for head CT examination is summarized in the 99 online supplement (supplemental Table S4). Weight data were available in all cases from the 100 electronic medical records. Height and gender data were recorded in 28 and 38 infants, respectively.

101 A tidal volume (VT) of 7 ml/kg was used to ventilate the casts, in one case based on ideal weight due 102 to a lower than normal real weight. 103 104 Image analysis 105 All images were anonymized for analysis. Native Dicom images were converted to Nifti format. The 106 nasal airway structures were segmented from the nares to the epiglottis, using an active contour 107 algorithm in itk-SNAP software (26) (www.itksnap.org). A representative example is shown in 108 Figure 1. The accuracy of the segmentation was visually examined and manually edited when 109 necessary by an Ear-Nose-Throat specialist (NA). The resulting segmented image was converted to a 110 mesh. A 3-dimensional model of the nasal airways was then produced with a 3D printer (Makerbot, 111 Replicator2, New York, USA) with polylactide using Meshmixer software (www.meshmixer.com) with 112 an accuracy of xy: 11 μm; z: 2.5 μm. The accuracy of the 3D-printed casts compared to the initial CT 113 image was verified in one case by CT scanning the cast, followed by image segmentation (3). 114 Comparison to the initially segmented image, qualitatively by overlaying images showed a quasi- 115 perfect match and a volume difference of 0.3 %. 116 117 The nasal airway passages were segmented and the volume, surface area, and various shape 118 descriptors were measured with Imagej software (www.imagej.nih.gov), using the ’3D Imagej Suite’ 119 plugins (https://github.com/mcib3d). Sparseness was defined as the ratio of the volume of a fitted 120 ellipsoid (Fto that of the 3D segmented image (supplemental Fig. S1). Flatness was defined as the 121 ratio of the second axis to the third axis of the ellipsoid. Elongation was defined as the ratio of the 122 first to the second axis of the ellipsoid. Sphericity was defined as:

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. ( ) 123 Sphericity= (Eq. 1) 124

125 Where Vaw is the volume of the segmented upper airways and Saw is the surface area. The theoretical 126 background of these measures is given in: (18). 127 128 Experimental setup 129 Rheological measurements of the upper airway casts were performed with custom-made equipment 130 (Fig. 1). Baseline measurements were recorded with the oscillatory signal only, without simulated

131 breathing (R0). Tidal excursions were generated by a 20-cm-diam. Subwoofer loudspeaker (SRP 2030, 132 Somogyi Audio Line, Budapest, Hungary) at three different respiratory rates (33, 45 and 57

-1 133 cycles·min ). An estimated VT (7 ml/kg) was applied at each rate. Measurements were repeated at

134 half of the estimated VT (Fig. 2). 135 136 Small-amplitude (0.5 hPa) oscillations at 16 Hz and the superimposed simulated breathing pattern 137 were generated by the loudspeaker. The combined V’ signal was delivered to the pharyngeal opening 138 of the cast via a custom-made pneumotachograph and a modification of the wave-tube oscillometer 139 for infants (9) (length: 10 cm, internal diameter: 8 mm) measuring the input impedance of the naso- 140 pharyngeal cast through a conic adaptor (length: 30 mm, average diameter: 10 mm). Leakage was 141 prevented by a thin rim of silicone putty applied at the ends of the conic adaptor. Difference in the 142 cross-sectional areas between the adaptor and the pharyngeal opening of the cast was negligible. 143 The wave-tube and the pneumotachograph were equipped by identical pressure sensors (Honeywell 144 model 26PCAFA6D, Golden Valley, MN, USA). The pressure and flow signals were low-pass filtered at 145 50 Hz and sampled at a rate of 512 s-1. 146 147 Data analysis

148 Input impedance of the cast (Zn) was calculated based on the auto- and cross-power spectra of the 149 wave-tube’s lateral pressures using the fast Fourier transform. The pressure signals were bandpass-

150 filtered in the 16±2 Hz frequency range of the spectra. The Zn values were computed for 4 oscillation

151 cycles (0.0625 s each) and a moving average was calculated over the time span of 0.25 s. Zn is

152 expressed in terms of resistance (Rn) and reactance (Xn). Volume (V) was integrated from V’using the 153 trapezoidal approach, while V” was calculated as the derivative of V’ from individual datapoints, by 154 simple one-sided difference quotients. 155

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 156 To characterize the relation between Rn and V’ (Fig. 4), two separate linear equations were fitted 157 below and above a characteristic breakpoint. For the segment below the breakpoint (1 mL.s-1

158 V’bp):

159 ln R = k ×lnV′+k (Eq. 2)

160 For the segment above the breakpoint (V’> V’bp):

161 ln R = (k +k)×(lnV −lnV′)+lnR (Eq. 3)

162 Where Rbp is the breakpoint resistance at V’ = V’bp

163

164 Estimation of Reynolds number (Re)

165 The volume (V) of each cast was divided by the characteristic pathway length (l) resulting in a rough 166 estimate of average cross-sectional area (A) (Eq. 4). Volumetric flow rate at breakpoint or at peak V’ 167 was divided by A, to obtain linear velocity (u) (Eq. 5). Re was calculated with the equation for smooth 168 cylindrical tubes, taking kinematic viscosity (ν) of air as 1.849·10-5 m2·s-1 (at 25 °C) (Eq. 6).

169 A= (Eq. 4.) 170 u= (Eq. 5.) × 171 𝑅𝑒 = (Eq. 6.) 172 173 174 In vivo measurements

175 Oscillometric measurements of the respiratory system impedance (Zrs) were performed in healthy 176 term newborns with a custom-made wave-tube setup, in a setting similar to described previously 177 (Hantos et al. 2015, Gray et al. 2019). The study protocol was approved by the Institutional Clinical 178 Ethics Comittee of the University of Szeged (91/2011). Written informed consent and assent was 179 obtained from all parents prior to data collection. A 16-Hz sine wave was applied as the oscillatory

180 signal, and Zrs was estimated with the same signal processing technique as that used in the casts (see

181 above) and expressed as total respiratory resistance (Rrs) and reactance (Xrs). The measurements 182 were performed before the 4th postpartum day, during quiet natural sleep. Exclusion criteria were: 183 1- poor cooperation; 2- lack of steady-state breathing; 3- nasal obstruction before or during 184 measurement; 4- leakage around the face mask during measurement; 5- laryngeal breaking or 185 inspiratory flow limitation detected during the measurements. A minimum of 5 steady-state,

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 186 artefact-free breathing cycles was taken for analysis. A piecewise linear regression equation was

187 fitted to the relationship between respiratory resistance (Rrs) and V’, in the same manner as for the 188 nasal airway casts. 189

190 Statistical analysis

191 Data are expressed as median (interquartile range) unless stated otherwise. Relationships between

192 Rn and V’ and V” were examined by linear regression and piecewise linear regression, for expiratory 193 and inspiratory data (10). The relationship between structural and impedance data was assessed by 194 Pearson’s correlation coefficient. Statistical analysis was performed using the open-source R 3.5.1 195 software (R Foundation for Statistical Computing, Vienna, Austria, 2019), using the standard built-in 196 and ‘segmented’ (1.0-0) packages. A p-value < 0.05 was considered as significant.

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 197 RESULTS 198 199 A total of 46 casts were measured. The study population characteristics are summarized in Table 1. 200 One cast was excluded because of apparent bilateral nasal obstruction, confirmed by re-assessment

201 of the CT images, which resulted in extremely high Rn values. 202

203 Intrabreath changes in Rn and Xn as functions of V’ and V’’ are illustrated in Figure 3. ReE shifted to

204 higher values from R0 even at the smallest V”. The fluctuations of Xn were small and largely

205 unaffected by changes in V’ and V” (see also Fig. S6). For all casts, a median value of shift in ReE of

206 47% (range 41-52%) was observed at the lowest respiratory rate and VT. A very strong linear 2 207 relationship was observed between ReE and V”eE in each set of cast measurements: r =0.994 (Q1 – 208 Q3: 0.988 – 0.996, p<0.001) with considerable inter-individual variability in the coefficients of 209 regression (supplemental Fig. S2). The intercept of the linear regression was found to be a close

210 estimate of R0, characterized by a median of relative bias of -4.5% (-12 – 6%). 211

212 A characteristic nonlinear relationship was found between Rn and V’, exhibiting segmental linearity 213 and a prominent breakpoint after logarithmic transformation (Fig. 4). The adjusted r2 values for the 214 fitted piecewise linear model were 0.984 (0.974-0.989) and 0.984 (0.974-0.988) for the expiratory

215 and inspiratory phase, respectively, all frequencies and volumes included. V’bp during the expiratory 216 phase had a median value of 0.041 L·s-1 (0.028-0.058) for the entire dataset. The slope of the first 217 segment (k1) was 0.0426 (0.0262-0.0649), while slope of the second segment (k1+k2) was steeper,

218 with a median of 0.9572 (0.857-1.101). Similar piecewise linear Rrs vs V’ relationships were observed 219 in the in vivo measurements (supplemental Fig. S3). 220

2 221 V’bp was found to be linearly related to V” (r =0.96, p<0.001) with increasing residual errors at higher

222 values (Fig 5). The in vivo data exhibited a similar V’bp vs V” relationship at slightly lower values of

223 V’bp. 224

225 The estimated Re at maximal flow was 118.4 (91.3-154.9), while Re at V’bp at maximum respiratory

226 rate (0.95 Hz) and VT was 60.8 (47.3-81.4). Figure 6 shows the relationships between the shape

227 indices of the nasal airways and Re. The Re at V’bp (Re(V’bp)) was found to be inversely proportional to 228 the sparseness of the airway (r2 = 0.43, p<0.001) and directly proportional to its flatness (r2 = 0.31, 229 p<0.001). Other structural descriptors (tortuosity, elongation or sphericity) had no connection with

230 Re(V’bp) (p>0.10). X0 showed moderate correlation with sparseness and was found to be inversely

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 2 2 231 proportional to flatness (r = 0.24 and r = 0.14, respectively, p<0.05). R0 correlated weakly with 232 sparseness (r2=0.09, p<0.05) and had no correlation with flatness (r2= 0.05, p>0.10). 233

234 To estimate R0 based on the intrabreath R-V’ loops (Fig. 7, top) the slope of the fitted line was

235 determined between ReE and Rn at maximum inspiratory flow (RV’maxI). The slope of this linear fit

236 remained constant across the different respiratory rates and VT’s. When this linearly approximated

237 V’-dependent increase in Rn was compared to the V”-dependent shift in ReE (Fig. 7, bottom) a strong

238 linear relationship was found. By utilising this relationship R0 can be estimated from a single intra- 239 breath impedance measurement:

240 R =R −V" ×𝑐× (Eq. 7.)

241 Where c is a correction factor with a value of 0.0646 s-1, that is the slope determined from the 242 expiratory limb in Fig. 7 (bottom). Strong relationship with a similar slope (0.0709 s-1, p<0.001) was

243 also observed for the inspiratory limb (data not shown). This estimation of R0 is hence independent 244 of respiratory rate and tidal volume.

245

246 The relative error of measured and corrected ReE with respect to the R0 at each setting of the

247 respirator is shown in Fig. 8. Measured ReE was significantly (p<0.001) higher than corrected ReE at

248 each setting with increasing differences at higher frequency and VT. After applying the mathematical

249 correction in ReE to the in vivo measurements, the end-inspiratory R (ReI) decreased by 33% (9.5 -

250 70%, p<0.001), while ReE dropped 19% (1.6 - 33%, p<0.001) (supplemental Fig. S3).

251 X0 had positive values in all casts, indicating the presence of inertance in the rigid upper airway casts.

252 The overall shape of Xn-V’ loops mirrored the pattern of Rn-V’ loops (supplemental Fig. S6); however,

253 the changes of Xn were smaller and not as regular as seen for Rn. Xn decreased significantly (p<0.001)

254 when simulated breathing was applied (supplemental Fig. S7). End-expiratory Xn (XeE) was found to

255 be somewhat lower than X0, indicating that V” has some effect on Xn; however, this effect cannot be

256 described by a simple linear relationship as it was demonstrated for ReE. Xn was found to be V’-

257 dependent: the lowest values of Xn were measured at peak inspiratory and expiratory flows (XV’maxI

258 and XV’maxE). However, the decrease was independent from the actual values of V’max.

259 The "mirroring” pattern of Xrs-V’ loops was visible for most of the in vivo measurements in healthy 260 newborns (supplemental Fig. S8), despite the mean Xrs values are usually negative at 16 Hz.

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 261 Sometimes we observed increasing (less negative) Xrs values at peak V’-s – a phenomenon never 262 found in vitro.

263

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 264 DISCUSSION

265 The primary aim of this study was to examine the confounding effect of the nasal pathway during

266 oscillometric assessment of lung mechanics. The contribution of Rn to Rrs (especially during tidal 267 breathing) is a main problem in infant pulmonary function testing, but examining this effect is 268 difficult with non-invasive techniques. Therefore, we used anatomically faithful, although rigid upper 269 airway casts to measure Rn and simulate the effects of spontaneous breathing on this parameter in 270 vitro.

271 Validity of R0

272 We hypothesize that R0 can be the most appropriate outcome measure for comparing patients, since

273 it is the lowest R, unbiased by the dynamic effects of tidal breathing. Note that R0 was assessed, 274 instead of the unidirectional Poiseuille flow, with 16-Hz sinusoidal oscillations. This causes an

275 overestimation of Poiseuille R (RP) via the frequency dependence of resistance (4-6). We could 276 demonstrate a moderate correlation (r2=0.41) between the Womersley number and the ratio of

277 measured R0 to calculated RP, a phenomenon already described in straight tubes by Dorkin et al. In

278 fact, the R0 values were typically 10-30 times higher than RP (see : Fig. S5).

279 Although R0 is the lowest oscillatory R, it can be measured only during apnea, which may limit its

280 widespread use. R0 values in our nasal airway casts were systematically lower than a previously 281 published study in infants (8, 22). In these studies, infants were measured during apnea with low- 282 frequency oscillometry, and nasal resistance was estimated by applying a nasal cannula with a 283 manometer. The oscillatory frequency was higher in the present study (16 Hz sine wave vs. 0.5-20 Hz 284 pseudorandom signal) allowing us to use lower amplitude (18-20 ml/s vs 60-80 ml/s peak-to-peak) 285 while achieving the same signal-to-noise ratio. This amplitude represents ∼70% of the flow measured 286 during tidal breathing in infants, thus it is high enough to cause nonlinearities in the nasal airways. 287 We tested this effect in a subgroup (n=12) of our casts. Increasing the oscillatory flow to 28-32 ml/s

288 (peak-to-peak) resulted in an increase in R0 of 11% (8.7-16.5%). Additionally, some extra dissipation 289 can be produced by the collapsibility of the upper airways in vivo leading to even higher R values 290 (16).

291 Validity of ReE

292 If the nasal pathway acted as a pure linear resistor, the ReE would be independent from respiratory

293 rate and V’ and would thus be equal to R0. However, we found that ReE increased linearly with V”eE

294 and was considerably higher than R0 even at the lowest respiratory rate. Direct measurement of ReE

295 as well as ReI, are biased by the extra dissipation due to unstable V’ arising in the nasal pathway at

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 296 phase transitions. This phenomenon was described previously in tracheal models by Isabey and

297 coworkers (14, 15). We conclude that ReE alone may not be an appropriate estimate of R0. However,

298 serial measurements of ReE at different V” values enable a fair approximation, as the coordinate 299 intercept of the linear function.

300 Utility of Rn-V’ segmented power-law model

301 We found that the relation of Rn with V’ can be described by a segmented power-law equation. The 302 first segment had an almost negligible increase until a breakpoint followed by a more abrupt 303 elevation above the breakpoint. This non-linear behaviour of the P-V’ relationship in the nasal 304 airways may be related to a developing non-laminar flow regime (15, 20, 21, 24) and to singular 305 pressure losses at abrupt narrowings, or the so-called orifice effect (13). Both processes may

306 contribute to the sharper V’-dependent rise observed in Rn beyond V’bp. Our data also showed that

307 V’bp has a strong linear dependence on V”. Increasing V” may affect flow rheology by the re- 308 laminarisation of turbulent flow (11).

309 The effect of sharp narrowings in the nasal passages is reflected in the relation between certain

310 shape descriptors and Re(V’bp). Upper airway casts with higher sparseness had a relatively spacious 311 cavity with less wall irregularities and lower surface/volume ratio. Flatness on the other hand is an 312 indicator of relative narrowness of the nasal passage, mimicking a slit between two infinite parallel

313 plates. Sparse but not flat nasal cavities, acting as wide cylinders, had low Re(V’bp) values, suggesting 314 that this geometry is advantageous for the development of turbulent flow.

315 Despite the fact that V’bp correlated well with structural variables, the utility of V’bp and other

316 parameters of the segmented power-law model, remains limited in the estimation of R0, because of 317 the strong V”-dependence. This was verified in a small and selected group of healthy term newborns

318 even though there was a strong V’bp-V” relationship (Fig. 5) and the model fitted well for these in vivo 319 measurements (supplemental Fig. S3).

320 Geometrical estimation of R0 from a single Rn-V’ loop

321 We propose a method for correcting the shift in ReE, thus estimating R0, by the normalized flow-

322 dependent increase in R: (RV’maxI-ReE)/V’maxI. This method can be applied to a single set of intrabreath 323 oscillometric measurements, without the necessity of changing respiratory rate or tidal volume, as 324 performed in our simulations. Infant measurements showed that the effect of upper-airway non-

325 linearities are significant and represent up to 33% in ReI and 19% in ReE (supplemental Figur S4).

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 326 Extrapolation of Rrs data by using the equation derived from the cast measurements (Eq. 6) resulted

327 in a larger decrease in ReI than ReE, thereby increasing the tidal difference in Rrs (ΔR). Since ΔR has 328 been shown to be a sensitive measure of subtle alterations in peripheral homogeneity (1, 7), 329 application of a correction accounting for the V”-dependent effects would further increase the utility 330 of ΔR.

331 Dynamic changes in Xn and Xrs

332 We measured positive mean values of Xn, indicating the presence of inertance, an expected property

333 of the upper airways. The V’-dependent decrease in Xn can be explained by the decrease in apparent 334 inertance caused by the vortex formation at orifices (12, 17).

335 The patterns of Xrs change during the respiratory cycle were similar in the in vivo measurements,

336 although more variable than that of Xn, and the mean Xrs values were negative due to the presence of 337 elastic forces of the total respiratory system at 16 Hz. The compliant upper airway structures may 338 have added to this variability (while the orifice effects were still present); an extreme example of 339 inspiratory flow limitation (the Bernoulli effect) is demonstrated in Fig S8 (infant #11).

340 Study limitations

341 This study had some limitations. Since the CT sampling time was quite short (∼75-300 ms), we can 342 assume that the whole nasal pathway was reconstructed in the same phase of the respiratory cycle. 343 Nevertheless, since CT acquisition was not gated with respect to the respiratory phase, the within- 344 breath variation in the diameter of the soft tissue that may exist in vivo is not reflected in the 3D cast. 345 Although the fact that the vocal chord area and part of the oropharynx, more compliant structures of 346 the upper airways, were not included in the reconstructed upper airways must have substantially 347 reduced the intrabreath changes, this in turn imposed another limitation in the applicability of cast 348 measurements in the interpretation of the in vivo infant data. A further limitation was the rigid 349 material of the cast, as well as the surface texture that can be different from that of the upper airway 350 mucosa. Non-linearity originating from the compliance of some segments of the nasal pathway

351 cannot be modeled by this approach. Despite the rigidity of the casts, distortions in the Rn – V’ 352 relationship could be adequantly studied since the orifice effect can be considered the most

353 important contributor to the flow-dependence of Rn during tidal breathing.

354 A time windowing of 0.25 s was used during intrabreath oscillatory measurements. This means that 355 an average of 4 oscillatory cycles was used for impedance estimation. Decreasing windowing time to 356 a minimum of two cycles excessiveley decreased signal-to-noise ratio, which was especially critical in 357 the in vivo setting. The effect of increasing the windowing time was investigated in a subgroup of our

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 358 casts (n=12; data not shown). Increasing windowing time to 0.5 s led to higher values of ReE but

359 without much change in RV’maxI and RV’maxE. Although the increase in ReE was systematic, the intercept

360 of the linear ReE vs V”eE relationship did not change, so the estimation of R0 seems to be insensitive to 361 windowing time.

362

363 CONCLUSIONS

364 We studied R-V’ relationship in anatomically faithful rigid nasal airway casts during simulated 365 respiration. We found a characteristic nonlinear relationship between R and V’, exhibiting segmental 366 power-law behavior with a prominent breakpoint. This model was reproducible in a small group of

367 infants in vivo. We found a linear shift in ReE which was attributable to increasing values of V”. We

368 developed a geometrical approach to quantify intra-breath non-linearities in Rn, allowing to estimate

369 R0 from a single oscillometric measurement. Using the correction may reduce the masking effect of 370 the nonlinear upper airways on the changes in the intrathoracic R in future studies.

371

372

373

374

375 ACKNOWLEGDEMENTS

376 The authors wish to thank Raffaella Balzarini and Stanislas Borkowski for help with 3D printing of 377 upper airway casts.

378

379 FUNDING

380 Supported by Hungarian Scientific Research Fund grants K105403 and K128701, and by the 381 Amiqual4Home Equipex, via the ANR-11-EQPX-0002 grant.

382

383

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 384 Author Contributions: BR, ZH, and SB conceived the study; SB, TC, NA, CP,and LD selected eligible CT 385 scans and performed image segmentation; TC and KB: prepared and performed 3D printing; BR, GM, 386 ZH, and SB performed the in vitro measurements; ZG, GM, ZH, and BR developed a custom-made 387 measurement setup and data acquisition software; ZGY, BR, ZH, GM recruited infants and performed 388 in vivo measurements; BR and ZH analysed oscillometric data; SB performed nasal airway structural 389 data analysis; BR and TMT performed mathematical and statistical analysis; BR, ZH, and SB drafted 390 the manuscript. All authors have seen the submitted manuscript.

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 391 REFERENCES

392 1. Czovek D, Shackleton C, Hantos Z, Taylor K, Kumar A, Chacko A, Ware RS, Makan G, Radics 393 B, Gingl Z, and Sly PD. Tidal changes in respiratory resistance are sensitive indicators of airway 394 obstruction in children. Thorax 71: 907-915, 2016. 395 2. Davidson RN, Greig CA, Hussain A, and Saunders KB. Within-breath changes of airway 396 calibre in patients with airflow obstruction by continuous measurement of respiratory impedance. Br 397 J Dis Chest 80: 335-352, 1986. 398 3. Doorly DJ, Taylor DJ, and Schroter RC. Mechanics of airflow in the human nasal airways. 399 Respir Physiol Neurobiol 163: 100-110, 2008. 400 4. Dorkin HL, Jackson AC, Strieder DJ, and Dawson SV. Interaction of oscillatory and 401 unidirectional flows in straight tubes and an airway cast. J Appl Physiol Respir Environ Exerc Physiol 402 52: 1097-1105, 1982. 403 5. Finucane KE, Dawson SV, Phelan PD, and Mead J. Resistance of intrathoracic airways of 404 healthy subjects during periodic flow. J Appl Physiol 38: 517-530, 1975. 405 6. Franken H, Clement J, Cauberghs M, and Van de Woestijne KP. Oscillating flow of a viscous 406 compressible fluid through a rigid tube: a theoretical model. IEEE Trans Biomed Eng 28: 416-420, 407 1981. 408 7. Gray DM, Czovek D, McMillan L, Turkovic L, Stadler JAM, Vanker A, Radics BL, Gingl Z, Hall 409 GL, Sly PD, Zar HJ, and Hantos Z. Intra-breath measures of respiratory mechanics in healthy African 410 infants detect risk of respiratory illness in early life. Eur Respir J 53: 2019. 411 8. Hall GL, Hantos Z, Wildhaber JH, and Sly PD. Contribution of nasal pathways to low 412 frequency respiratory impedance in infants. Thorax 57: 396-399, 2002. 413 9. Hantos Z, Czovek D, Gyurkovits Z, Szabo H, Maar BA, Radics B, Virag K, Makan G, Orvos H, 414 Gingl Z, and Sly PD. Assessment of respiratory mechanics with forced oscillations in healthy 415 newborns. Pediatr Pulmonol 50: 344-352, 2015. 416 10. Hey EN, and Price JF. Nasal conductance and effective airway diameter. J Physiol 330: 429- 417 437, 1982. 418 11. Iida O, and Nagano Y. The relaminarization mechanisms of turbulent channel flow at low 419 Reynolds numbers. Flow, Turbulence and Combustion 60: 193-213, 1998. 420 12. Ingard U, and Ising H. Acoustic nonlinearity of an orifice. The journal of the Acoustical Society 421 of America 42: 6-17, 1967. 422 13. Ingram Jr RH, and Pedley TJ. Pressure-Flow Relationships in the Lungs. Comprehensive 423 Physiology 277-293, 2011. 424 14. Isabey D, and Chang HK. Steady and unsteady pressure-flow relationships in central airways. 425 J Appl Physiol Respir Environ Exerc Physiol 51: 1338-1348, 1981. 426 15. Isabey D, Chang HK, Delpuech C, Harf A, and Hatzfeld C. Dependence of central airway 427 resistance on frequency and tidal volume: a model study. J Appl Physiol (1985) 61: 113-126, 1986. 428 16. Jaeger MJ, and Matthys H. The pattern of flow in the upper human airways. Respir Physiol 6: 429 113-127, 1968. 430 17. Jing X, and Sun X. Sound-excited flow and acoustic nonlinearity at an orifice. Physics of Fluids 431 14: 268-276, 2002. 432 18. Kiwanuka FN, and Wilkinson MHF. Cluster Based Vector Attribute Filtering. In: Mathematical 433 Morphology and Its Applications to Signal and Image Processing, edited by Benediktsson JA, 434 Chanussot J, Najman L, and Talbot H. Cham: Springer International Publishing, 2015, p. 277-288. 435 19. Lorx A, Czovek D, Gingl Z, Makan G, Radics B, Bartusek D, Szigeti S, Gal J, Losonczy G, Sly 436 PD, and Hantos Z. Airway dynamics in COPD patients by within-breath impedance tracking: effects of 437 continuous positive airway pressure. Eur Respir J 49: 2017. 438 20. Pedley TJ, Schroter RC, and Sudlow MF. Energy losses and pressure drop in models of 439 human airways. Respir Physiol 9: 371-386, 1970. 440 21. Peslin R, Ying Y, Gallina C, and Duvivier C. Within-breath variations of forced oscillation 441 resistance in healthy subjects. Eur Respir J 5: 86-92, 1992.

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 442 22. Petak F, Hayden MJ, Hantos Z, and Sly PD. Volume dependence of respiratory impedance in 443 infants. Am J Respir Crit Care Med 156: 1172-1177, 1997. 444 23. Polgar G, and Kong GP. The nasal resistance of newborn infants. J Pediatr 67: 557-567, 1965. 445 24. Schroter RC, and Sudlow MF. Velocity profiles in models of human airways. J Physiol 202: 446 36P-37P, 1969. 447 25. Stocks J, and Godfrey S. Nasal resistance during infancy. Respir Physiol 34: 233-246, 1978. 448 26. Yushkevich PA, Piven J, Hazlett HC, Smith RG, Ho S, Gee JC, and Gerig G. User-guided 3D 449 active contour segmentation of anatomical structures: significantly improved efficiency and 450 reliability. Neuroimage 31: 1116-1128, 2006. 451

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 452 FIGURE LEGENDS 453 454 Figure 1. Left: Schematic illlustration of the experimental setup. Right: Transparent three- 455 dimensional (3D) reconstruction of the upper-airways, used as a sample for 3D-printing. 456

457 Figure 2. Time-series of two representative measurement setting. Small-amplitude oscillatory signal 458 (16 Hz) superimposed on the simulated tidal breathing. Top: 0.55 Hz breathing frequency with halved

459 tidal volume (VT/2). Bottom: 0.95 Hz respiratory rate with normal tidal volume (VT). Black line: 460 volume, gray line: flow (V’).

461 Figure 3. Resistance (Rn) and reactance (Xn) plotted against flow (V’) (left) and volume accelaration 462 (V”) (right) from a representative cast. Each set of coloured loops (see insets) corresponds to preset

463 breathing frequencies (0.55, 0.75 and 0.95 Hz) and tidal volumes (VT and VT/2). Closed and open

464 circles indicate the lowest oscillatory R (R0) and X (X0), respectively, determined without tidal flow 465 (V’=0).

466 Figure 4. Log-log plot of resistance (Rn) vs absolute value of flow (V’) during expiration from a

467 representative measurement (Setting: 0.55 Hz, halved tidal volume [VT/2]). A segmented linear 468 model with a breakpoint is fitted to the data, indicating power-law relationship with two exponents: 469 a lower exponent for the first segment and a higher exponent for the second segment (below and 470 above breakpoint, respectively).

471 Figure 5. Relationship between volume acceleration (V”) and flow at break point (V’bp) estimated at 472 different simulated breathing settings. Each colored circle represents a single measurement from all 473 (n=45) casts. In vivo measurement from each newborn (n=15, open circles) recorded during the first 474 3 days of life. 475

476 Figure 6. Correlation between the Reynolds number at breakpoint flow Re(V’bp) versus Sparseness 477 (left) and Flatness (right) of the casts. High Re can be found for casts characterised by low sparseness 478 and high flatness indicating that flow transition is delayed in narrow and flat upper airways 479 (dominance of viscous forces). Each point corresponds to an individual cast (setting: 0.95 Hz, normal 480 tidal volume).

481 Figure 7. Top: Resistance (Rn) versus volume acceleration (V”) plot from a representative cast. Open

482 circle represents the lowest oscillatory R (R0), black line with closed symbols represents Rn measured

483 with superimposed breathing at 0.95 Hz with full tidal volume (VT). Each data point is marked with a

Downloaded from journals.physiology.org/journal/jappl at Kings Col London Jrnls Sec (137.073.144.138) on July 29, 2020. 484 closed symbol. Dashed line marked with ”f” shows the slope of V’-dependent increase in R; dashed

485 line marked with ”a” represents the shift in the minimal resistance (R0) due to V”. Arrowheads

486 indicate inspiratory limb of the loops. Highest resistances occur at peak inspiratory flow (RV’maxI) and -1 487 at peak expiratory flow (RV’maxE). Bottom: The V”- dependent shift in ReI [(ReI-R0).V”eI ), i.e. slope ”a” -1 488 in top panel] plotted against V’-dependent increase in Rn [(RV’maxE-ReI.V’maxE ), slope ”f”], reflecting a 489 strong linear relationship. Each symbol represents a cast, measured at different respiratory rates at

490 full or halved tidal volume (VT and VT/2). 491

492 Figure 8. The relative error of measured (grey box) and corrected (open box) lowest resistances (ReE) 493 with respect to the oscillatory resistance without superimposed breathing (R0) at each setting of the 494 respirator. Respiratory rate varied from 0.55 Hz to 0.95 Hz, at full (VT, right panel) and halved (VT/2, 495 left panel) tidal volume. Measured R0 was significantly (p<0.001) higher than calculated R at each 496 setting.

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