| Background and objectiveAngle Class Ⅱ1 malocclusion is a common occlusal deformity in clinical practice,with an incidence of 15～20%.Mandibular retrognathia is the most common feature in Class II malocclusion,while maxillary protrusion is uncommon.Mandibular retrognathia is a condition in which the mandible is positioned more posteriorly in relation to the maxilla.As a result,the tongue,hyoid bone,and soft tissue attached to the mandible are displaced posteriorly,narrowing the upper airway,which in turn affects the ventilation function of patients.Severe cases may even lead to obstructive sleep apnea hypoventilation syndrome(OSAHS).Studies have shown that OSAHS patients with mandibular retrognathia have higher apnea index and respiratory disorder index.According to domestic and foreign statistical data,the incidence of OSAHS in children is 1.2%to 5.7%,which is mainly characterized by repeated pharyngeal airway collapse during sleep,resulting in airflow cessation,oxygen saturation,and sleep interruption.etc.,can lead to hyperactivity,inattention,daytime sleepiness,metabolic syndrome,cognitive deficits,and growth arrest in children.OSAHS is a disease caused by multiple factors,including the abnormal anatomical structure of the upper airway,abnormal neuromuscular activity,or the combination of other pathophysiological factors.Previous studies have found that the severity of OSAHS is highly correlated with upper airway airflow characteristics.From the perspective of aerodynamics,upper airway stenosis leads to airflow recirculation and negative intraluminal pressure in anatomically susceptible areas,which may lead to upper airway collapse.Therefore,studying the flow characteristics of the upper airway and evaluating the changes of parameters such as velocity and pressure caused by clinical treatment methods can predict the airway hydrodynamic characteristics of patients with mandibular retrognathia and the flow pattern after the clinical intervention,which is helpful for doctors to accurately locate the obstruction in patients,clarify the physical mechanism of the pathogenesis,and realize the purpose of transforming patients from empirical treatment to precise treatment.Materials and methods1.Influence of oral cavity preservation in upper airway model on airway hydrodynamic characteristicsTen patients(7 boys;3 girls;age 9.56 ± 2.88 years,BMI 19.11 ± 2.55 kg/m2)at the growth and development stage of Angle Class Ⅱ1 with mandibular retrognathia were randomly selected.The upper airway model of the preserved and non-preserved oral cavity were reconstructed by CBCT with 0.4 mm scanning thickness.The image threshold was set as-1024～-480 HU in MIMICS,and then the regions of interest in each CBCT section were segmtioned.Finally,two-dimensional segmented sets were then reconstructed and smoothed into a three-dimensional upper airway model,so as to create a CFD simulation of the respiratory air domain.The upper airway model without oral cavity preservation was obtained by subtracting the oral cavity part from the oral cavity model to ensure a single variable.Then,based on the conditions of mouth opening and mouth closing during simple nasal breathing,CFD simulations were performed on the upper airway models with and without the oral cavity,respectively.2.Numerical simulation of unsteady characteristics and quasi-steady approximation of human upper airway airflowAirflow in the human respiratory tract is inherently unsteady,that is,the airflow changes over time.In the case of steady flow,it is considered that the flow state does not change with time.In classical fluid mechanics,the strouhal number(St)and Reynolds number(Re)are the key dimensionless parameters to measure the unsteady characteristics of upper airway airflow in humans.The CFD unsteady and quasi-steady simulations of the upper airway models were carried out using the standard k-ω model,which was validated by in vitro reliability.The standard respiratory mode was set in the condition of average respiratory flow of 200 mL/s and respiratory cycle of 3 s(case 1,St=0.01,Re=899).Then,based on the standard working conditions,St=1 or Re=4000 were changed to generate different combined working conditions to simulate various unsteady respiratory flow phenomena.The boundary conditions of the quasi-steady simulation at each discrete time were set to the mean inlet flow velocity given by the unsteady breathing curve at the same time point.By comparing the pressure and flow velocity of unsteady and quasi-steady CFD simulations,it can be determined whether they were consistent,and the applicable conditions of quasi-steady simulation.3.Numerical simulation and functional evaluation of upper airway before and after Twin Block treatmentA total of 20 patients with mandibular retrognathia who were treated in the Stomatological Hospital of Shandong University were selected and included in the study,including 8 males and 12 females(age 10.67 ± 1.51 years old,BMI 17.52±2.26 kg/m2).The airflow information obtained by the oronasal thermistor was used as the boundary condition of the CFD simulation to analyze the effect of different breathing paths on the upper airway flow.The average surface pressure(Pavg),minimum pressure(Pmin),maximum pressure drop(ΔPmax),maximum resistance(Rmax),and maximum shear force(WSSmax)were calculated for nasopharynx,velopharynx and glossopharynx.Statistical analysis was performed using SPSS software,and for normally distributed data,paired t-test was used to compare the differences between T1 and T2.If they did not conform to normal distribution,the Wilcoxon signed-rank test was used for comparison.P<0.05 indicates a significant difference.Pearson correlation analysis was used to analyze the correlation between OAHI and Pmin,ΔPmax,Rmax and WSSmax.4.The mechanism of upper airway collapse and the mechanical mechanism of Twin Block treatmentBy 3D printing resin and soft glue integrated upper airway model before and after TB treatment,the boundary conditions of upper airway soft tissue collapse and the biomechanical parameters of oropharyngeal soft tissue were obtained by in vitro model experiments.Then the fluid-structure interaction model of the upper airway and the oropharyngeal tissue were established.The maximum negative pressure,maximum flow velocity,and maximum oropharyngeal resistance of the upper airway before and after treatment were calculated in the fluid domain.The maximum deformation of the upper airway,AR and α were calculated in the solid domain at each breath time to determine the location of airway collapse,and to verify the reliability of the fluid-structure interaction simulation based according to the displacement.Results1.The effect of oral structure preservation and closed and open breathing on airflow in the upper airwayThe maximum difference between the high-flow(heavy breathing)and low-flow(light breathing)airflow predicted by standard k-ω model and the measured data in vitro was within 20%.CFD studies have shown that the internal flow velocity of the open mouth retained in the upper airway was almost zero.Under the condition of closed-mouth breathing,the difference in pressure of the upper airway was less than 3%,and the difference in velocity was less than 6%;under the condition of open-mouth breathing,the difference in upper airway pressure with or without retention was less than 15%,and the difference in velocity was less than 11%.2.Numerical simulation of unsteady characteristics and quasi-steady approximation of human upper airway airflowWhen St=0.01,the hysteresis loop was not significant.The closer the volume flow was to the peak,the more consistent the pressure and velocity profiles of unsteady simulation were with those of quasi-steady simulation,and the more similar the mechanical profiles with the same tidal volume at the acceleration and deceleration stages were.However,when St=1,the hysteresis loop was significant,and there was a significant difference between unsteady and quasi-stationary results.The maximum difference in pressure and velocity occurred near the respiratory transition point.When St<0.04,the average relative difference between unsteady and quasi-steady simulated pressure was less than 20%,and the hysteresis effect of unsteady flow was also small.With the continuous increase of Re,the relative difference did not increase significantly even with the increase of one order of magnitude.3.Numerical simulation and functional evaluation of the upper airway before and after TB treatment3.1 Morphological featuresAfter TB treatment,the average increments of the cross-sectional areas of the nasopharynx,velopharynx,and glossopharynx were 58.160 mm2,127.702 mm2 and 73.412mm2,respectively.And the velopharyngeal and glossopharyngeal volumes increased by 5957.246 mm3 and 1896.654 mm3,respectively.Only the velopharyngeal volume changes were statistically significant.The hyoid bone moved forward 2.443 mm(P<0.05).The Pearson correlation test showed that the changes in airway cross-sectional area,volume,and sagittal displacement of the hyoid bone were negatively correlated with OAHI,but there was no statistically significant correlation.3.2 Fluid mechanics characteristicsDuring nasal breathing,the minimum pressure of the upper airway was located in the glossopharynx,but the maximum pressure drop and resistance were located in the velopharynx.After TB,with the improvement of the morphology of the upper airway,the pressure drop,resistance and shear force of the velopharynx and glossopharynx significantly decreased compared with that before treatment(P<0.05).Pearson correlation test showed that OAHI index was negatively correlated with upper airway internal pressure,and positively correlated with upper airway pressure drop,resistance and maximum shear force,especially velopharyngeal resistance.For patients with obvious mouth breathing,the minimum pressure of the upper airway before treatment was also located in the glossopharynx,and the hydrodynamic parameters in the glossopharynx were improved more significantly after treatment.The correlation test showed that the OAHI index was significantly positively correlated with the upper airway glossopharyngeal pressure drop and resistance.4.The mechanism of upper airway collapse and the mechanical mechanism of TB treatment4.1 Upper airway fluid domain before and after TB treatmentAfter TB treatment,the maximum velocity of the upper airway decreased from 58.01 m/s before treatment to 46.16 m/s,and the maximum velocity of oropharynx decreased from 33.62 m/s to 28.26 m/s.Before treatment,the maximum negative pressure of oropharynx was located in the posterior wall,and the pressure gradient was larger than that of other parts.After treatment,the maximum negative pressure was limited to a small area of the anterior oropharyngeal wall,which decreased from-2741.81 Pa to-1767.54 Pa,and the pressure gradient also decreased significantly.The maximum resistance of upper airway and oropharynx was different,the former decreased from 1.45 Pa/mL/s to 0.92 Pa/mL/s,and the latter decreased from 0.38 Pa/mL/s to 0.21 Pa/mL/s.4.2 Oropharyngeal domain before and after TB treatmentBefore and after the treatment,the largest deformation parts were located in the posterior wall of the oropharynx.The maximum deformation area was not the location of the initial minimum cross-section,but near the minimum pressure.Compared with the upper and lower sections of the oropharynx,it was also the location with the largest longitudinal pressure difference.After TB treatment,the maximum deformation was reduced from 3.44 mm to less than 1 mm,which was reduced by more than 70%.The compliance of oropharyngeal soft tissue decreased from 0.048 mm2/Pa before treatment to 0.036 mm2/Pa after treatment.The Pearson correlation test showed that a was significantly positively correlated with the pressure drop(r=0.687,P<0.05).The closer the a value was to the range of 1,the smaller the oropharyngeal pressure drop was.And the larger the AR,the smaller the maximum negative pressure,and there was a significant negative correlation between the two(r=0.718,P<0.05).The in vitro experimental data were in good agreement with the results of the fluidstructure interaction simulation,except that the difference was slightly larger at the initial stage of inspiration,and the maximum difference was less than 20%.Conclusions1.It is demonstrated that the standard k-ω model can achieve reliable prediction of upper airway respiratory flow based on the establishment of an in vitro experiment platform.For children using only nasal breathing,it is reasonable to ignore the oral CFD simulation.2.The Strouhal number is a key parameter for judging whether the unsteady effect of the upper airway respiratory process is significant or not.When St ≤0.04,the hysteresis effect is not significant,the pressure of unsteady simulation and quasi-steady simulation tends to be consistent,and the quasi-steady simulation can replace unsteady simulation in the whole breathing cycle.3.Based on upper airway fluid dynamics simulation and functional evaluation,it is shown that TB treatment can significantly improve the ventilation function of patients with mandibular retrognathia.Compared with morphological parameters,hydrodynamic parameters are more suitable for evaluating the treatment effect of OSAHS.4.Based on the method of bidirectional fluid-structure interaction simulation,it is shown that the collapse site of the upper airway in children with mandibular retrognathia is not necessarily consistent with the narrowest location of the upper airway.The airway crosssectional shape and minimum pressure play a crucial role in influencing the collapse of the upper airway. |
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