- Email: [email protected]
Phase analysis in high-frequency oscillation
Medical Engineering & Physics 20 (1998) 452–457
Phase analysis in high-frequency oscillation S. Lee, R. Blowes, A.D. Milner
*
Newborn Respiratory Unit, St Thomas’ Hospital, London SE1 7EH, UK Received 2 December 1997; accepted 20 April 1998
Abstract In an oscillating system driven by a sine wave pump, the resonance frequency of the respiratory system can be determined using phase analysis. At resonance frequency, when elastance and inertance cancel out, flow becomes in-phase with resistance. In premature infants with respiratory distress syndrome, owing to surfactant deficiency, localized areas of hyperinflation and collapse develop, resulting in complex changes in overall pulmonary mechanics. We investigated the effect of measuring resonance frequency of the respiratory system by phase analysis at different points of the respiratory cycle: end of inspiration, end of expiration, mid-inspiration and mid-expiration. Ten ventilated premature infants with respiratory distress syndrome were studied, gestational age ranged from 24 to 30 weeks (mean 27.6 weeks) and birth weight ranged from 0.7 to 1.505 kg (mean 0.984 kg). Results: The resonance frequency was consistently higher when measured at the end of inspiration compared with the end of expiration. The expected trend of phase variation, that is, negative below the resonance frequency and positive above, was most consistently found when analysis was done at the end of inspiration. Conclusions: These findings were most likely a result of the complexity of pulmonary mechanics in the surfactant-deficient lungs, rendering the single compartment model we based our theory on inadequate. However, phase analysis performed at the end of inspiration seemed to produce the most reliable and consistent results. 1998 IPEM. Published by Elsevier Science Ltd. All rights reserved. Keywords: High-frequency oscillation; Neonates; Phase analysis
1. Introduction High-frequency oscillatory ventilation in neonatal practice has become widely advocated over the past 10 years [1,2]. The traditional frequency used for oscillation is 10 Hz. We theorized that potential benefits can be gained by oscillating neonates with the resonance frequency of their respiratory system through achieving more efficient ventilation. The resonance frequency of the respiratory system is defined as the frequency at which elastance and inertance cancel out and should, in theory, be the frequency at which oscillatory ventilation is most efficient [3]. This frequency is remarkably constant at approximately 5–6 Hz for both healthy adults and infants [4,5]. Expanding from the principles of the forced oscillatory techniques for measuring respiratory impedance [6–9], we devised a method using phase analysis to measure the resonance frequency of the respiratory system. Our theory was based on a single com-
* Corresponding author.
partment model, and in order to apply our theory in a clinical setting, we examined the effect of measuring the resonance frequency at various points of the respiratory cycle where the lungs are at different stages of expansion and deflation, in neonates with respiratory distress syndrome. Respiratory distress syndrome was chosen, simply because it is one of the most common conditions leading to respiratory morbidity requiring assisted ventilation in neonatal practice.
2. Theory In an oscillating system, if the respiratory system is modelled as a single compartment, its overall impedance can be regarded as the composite of three components. These are: (1) resistance of the respiratory system, which is mainly due to airway resistance, and is a function of the radius of the airway; (2) elastance, which is the reciprocal of compliance and is a function of the stiffness of the pulmonary tissue and chest wall; (3) inertance, which is largely composed of the force opposing acceler-
1350-4533/98/$19.00 1998 IPEM. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 0 - 4 5 3 3 ( 9 8 ) 0 0 0 4 2 - 3
S. Lee et al. / Medical Engineering & Physics 20 (1998) 452–457
ation of gas in the respiratory system. Unlike resistance, inertance and elastance are reactive components, i.e. their effect is dependent on the frequency of ventilation. It is apparent, therefore, that the overall impedance of the respiratory system changes with the frequency of ventilation [8]. When a driving force is applied to the respiratory system, a gas flow is created. The interaction between this flow and the system impedance generates pressure through the dissipation of energy. As impedance varies with ventilation frequency, the amplitude of the resultant pressure will vary. More importantly, the phase difference between flow and pressure will also vary. The single compartment model was a direct analogy in the classical resonant circuit of electrical AC theory [8,10] (Scheme 1). The voltage, V, developed across a circuit composed of resistance R, capacitance C and inertance L; driven by a current I is given by the formula: V = RI + LdI/dt + 1/C兰Idt
(1)
where = 2f, the angular frequency. In the resistor, V and I are in phase. In the inductor, V leads I by 90° and in the capacitor, V lags I by 90°. Thus the voltages in these two components are 180° out of phase. At the frequency where L = 1/C, the inductive and capacitive terms cancel out, thus resistance is the only impedance to flow and V and I are in phase. By definition, this is the resonance frequency, f0.
L = 1/C⇒0 = √(1/LC)⇒f0 = (1/2)√(1/LC)
(2)
3. Methods and patients High-frequency oscillation was provided by a custombuilt piston-based oscillator that had an oscillating frequency range of 2–30 Hz and a capacity of delivering constant tidal volumes of between 2 and 20 ml, by adjusting a movable fulcrum on the camshaft. A sine– cosine electrical generator connected to the cam of the system produced a sinusoidal electrical signal that represented the changes in piston position. Rotating the sine–cosine generator on its own axis allowed us to alter the phase relationship between the electrical output signal and the piston position if necessary. For the purpose of this study, the output signal was rotated 90° from the original position, thereby aligning it in phase with flow. Mean airway pressure support was provided by a conventional ventilator (either Sechrist Infant ventilator, model IV-100B or SLE 2000 Infant ventilator) on the continuous positive airway pressure mode; with the oscillator connected to the suction port at the patient manifold (Fig. 1). Changes in airway opening pressure were monitored at the proximal end of the endotracheal tube using a Validyne pressure transducer (MP15-20). The frequency response has been tested and over the range of 14–26 Hz, the response was within 7%. The output signal from the oscillator, together with the signal representing the changes of airway opening pressure were recorded via a frequency-modulated tape recorder onto magnetic tape. The signals from the magnetic tape were then sampled at 2000 Hz, using a digital data acquisition card with an anti-alias filtering device. The data was stored on computer hard disk. Phase analyses were performed on four set points of the respiratory
Eq. (1) can be rewritten in terms of the respiratory system as follows: Pmouth = RrsV⬘ + IrsV⬙ + (1/Crs)V
(3)
where Pmouth is mouth pressure; Rrs is resistance; Irs is inertance; Crs is compliance (reciprocal of elastance); V is volume; V⬘ is flow; and V⬙ is the time derivative of flow. Therefore, at the frequency where Irs = 1/Crs, resonance occurs with two important effects: 1. mouth pressure is in phase with flow; 2. the only impedance to flow is resistance, thus ventilation should be more efficient.
Scheme 1.
453
Fig. 1.
Schematic representation of ventilatory circuit.
454
S. Lee et al. / Medical Engineering & Physics 20 (1998) 452–457
cycle; mid-inspiration, end of inspiration, mid-expiration and end of expiration, using a custom-built computer program; by identifying the corresponding points on the two traces (Fig. 2). Ten premature ventilated infants with respiratory distress syndrome were recruited into the study. Gestational age ranged from 24 to 30 weeks (mean 27.6 weeks). Birth weight ranged from 0.7 to 1.505 kg (mean 0.984 kg). Informed written consent was obtained from at least one parent and the study was approved by the Ethics Committee of West Lambeth Health Authority. Each infant was oscillated from 8 to 30 Hz and back down to 8 Hz. This run was repeated to produce a measure of reproducibility. Mean airway pressure used in each case was 2 cmH2O higher than that employed during conventional ventilation. Volume delivery was set at 4 ml in all 10 cases.
4. Results All 10 infants completed the study with no adverse effects. The linear relationship between the phase difference and increasing oscillating frequencies was most consistently seen when phase analysis was performed at the end of inspiration. The expected trend, that is, negative below the resonance frequency and positive above, becoming more positive as frequency increases further was also most consistently observed at this point. We took the resonance frequency in this study as the frequency at which phase difference is closest to zero. The distribution of phase differences with varying oscillating frequencies is demonstrated in graph form in Fig. 3. The general trend of phase difference, that is, negative below the resonance frequency, and positive above, was seen
Fig. 2. A screen from our phase analysis program, showing phase analysis performed at four points of the respiratory cycle: top of breath, mid-inspiration, mid-expiration and bottom of breath. Corresponding points from the driving trace and the mouth pressure trace are matched and the phase difference calculated. In this case, the phase difference at the top of breath is 0° at an oscillating frequency of 20 Hz.
in most of the cases studied. The resonance frequencies found in all 10 infants at the four chosen points of the respiratory cycle are summarized in Table 1. In eight out of 10 cases, the resonance frequency was lowest at the end of expiration. This frequency was consistently higher when measured at the end of inspiration compared with at the end of expiration.
5. Discussion The relationship between resonance frequency, inertance and compliance can be summarized using the following equation [4] (cf. Eq. (2): 2f = 1/√(IC)
(4)
where f is the resonance frequency; I is inertance and C is compliance. At the end of inspiration, when the thoracic gas volume is relatively high, elastance or elastic recoil; the natural tendency for a stretched object to return to the resting, unstretched state is high. Compliance, being the reciprocal of elastance, is therefore low. As a result of a drop in C in the above equation, f increases (see Eq. (4)). The volume of air in the lungs is also at its maximum at the end of inspiration. In theory, this may cause an increase in I and therefore a decrease in f. However, the tidal volume in our premature recruits is extremely small. Consequently, the resultant changes in inertance is also relatively small. As a result, the resonance frequency measured at the end of inspiration is expected to be higher, when elastance is high and the absolute increase in lung volume and therefore inertance, is relatively insignificant; compared with that measured at the end of expiration. It becomes much more difficult to analyse and understand the measurements taken at mid-inspiratory and mid-expiratory points. The single compartment model on which we based our theory is not ideal when dealing with the respiratory system in premature infants with respiratory distress syndrome. In the surfactant-deficient state, the lungs become an inhomogenous complex structure with localized areas of consolidation and hyperinflation. As a result, the reproducibility of measurements at these points becomes unreliable. By definition, flow is in phase with resistance and 90° out of phase with the driving pressure. However after rotating the output signal through 90°, driving pressure becomes in-phase with flow. Below the resonance frequency, the (1/Crs)V component dominates in Eq. (3), where V represents the volume. Therefore, mouth pressure (or the resultant pressure) lags the driving pressure, resulting in a negative phase difference. Above the resonance frequency, the IrsV⬙ component dominates, where V⬙ is the time derivative of flow. Mouth pressure
S. Lee et al. / Medical Engineering & Physics 20 (1998) 452–457
455
Table 1 Summary of resonance frequencies found in all 10 babies (1 and 2 represents first and second run, respectively) Baby
One
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ten
Top 1 Top 2 Bottom 1 Bottom 2 Mid-inspiration 1 Mid-inspiration 2 Mid-expiration 1 Mid-expiration 2
22 22 19 15 21 22 24 24
20 20 17 17 19 19 21 20
16 15 10 9 14 15 19 19
20 19 15 9 20 19 19 17
20 20 9 19 19 20 21 17
17 17 15 14 16 16 18 18
22 22 17 17 20 21 20 20
23 22 19 18 16 16 9 8
17 16 13 13 15 15 17 16
12 12 9 16 9 9 8 14
Fig. 3.
Graphic representation of phase variation in babies 1–10.
now leads driving pressure resulting in a positive phase difference. At resonance frequency, when Irs and Crs cancel out, Pmouth = RrsV⬘, i.e. mouth pressure is in phase with driving pressure or phase difference is zero. In our study, it was not always possible to produce this expected trend of variation in phase difference with changing oscillating frequencies when measurements were done at our four chosen points in the respiratory cycle. Again, this inconsistency is probably due to the complex variation in pulmonary mechanics in the diseased lungs. However, we found that this trend was most consistently found when measurements were performed at the end of inspiration.
6. Conclusion Due to the complexity of the pulmonary mechanics in respiratory distress syndrome, the single compartment model on which we based our theory was not entirely fitting. However, phase analysis performed at the end of inspiration does provide us with the most accurate and reproducible results for the measurement of resonance frequency of the respiratory system. High-frequency oscillatory ventilation (HFOV) at resonance frequency could in theory provide more efficient ventilation compared with the conventional 10 Hz, since by definition, at this frequency, elastance and inertance cancel out.
456
S. Lee et al. / Medical Engineering & Physics 20 (1998) 452–457
Fig. 3.
Elastance is one of the major contributors to difficulty in ventilation in the surfactant-deficient lungs in premature neonates. A reliable method for measuring resonance frequency would certainly help towards designing a clinical trial to compare HFOV at resonance frequency of the respiratory system and at the conventional 10 Hz.
Acknowledgements Financial support for this project was gratefully received from Tommy’s Campaign, UK.
Continued.
References [1] Gertsmann DR, Minton D, Stoddard RA, Meredith KS, Monaco F, Bertrand JM, Batlisti O, Langhendries JP, Francois A, Clark RH. The PROVO Multicentre Early High Frequency Oscillatory Ventilation Trial: improved pulmonary and clinical outcome in respiratory distress syndrome. Pediatrics 1996;98:1044–57. [2] Clark RH, Gertsmann DR, Null DM, DeLemos RA. Prospective randomised comparison of high frequency oscillatory and conventional ventilation in respiratory distress syndrome. Pediatrics 1992;89:5–12. [3] Stocks J, Sly P, Tepper R, Morgan W. Infant respiratory function testing. USA: J. Wiley and Sons, Inc., 1996;8–9. [4] Mead J. Measurement of inertia of lungs at increased ambient pressure. Journal of Applied Physiology 1956;9:208–12.
S. Lee et al. / Medical Engineering & Physics 20 (1998) 452–457
[5] Mead J. Contribution of compliance of airways to frequencydependent behaviour of lungs. Journal of Applied Physiology 1969;5:670–3. [6] Cotes JE. Lung function assessment and application in medicine, 5th ed. Blackwell Scientific Publications, 1993;169–71. [7] Von Gierke HE, Oestriecher HL, Franke EK, Parrack HO, Von Wittern WW. Physics of vibrations in living tissues. Journal of Applied Physiology 1952;4:886–900. [8] DuBois AB, Brody AW, Lewis DH, Franklin Bergess JR. Oscil-
457
lation mechanics of lungs and chest in man. Journal of Applied Physiology 1956;8:587–94. [9] Zwart A, Peslin R. Mechanical respiratory impedance: the forced oscillatory method. Contributions to the workshop held for the European Commission on 18–19 June 1990, Antwerp, Belgium. European Respiration 1991;RevI:131–237. [10] Suprynowicz V. Introduction to electronics. USA: Addison–Wesley Publishing Company, 1966:91–3.
Phase analysis in high-frequency oscillation S. Lee, R. Blowes, A.D. Milner
*
Newborn Respiratory Unit, St Thomas’ Hospital, London SE1 7EH, UK Received 2 December 1997; accepted 20 April 1998
Abstract In an oscillating system driven by a sine wave pump, the resonance frequency of the respiratory system can be determined using phase analysis. At resonance frequency, when elastance and inertance cancel out, flow becomes in-phase with resistance. In premature infants with respiratory distress syndrome, owing to surfactant deficiency, localized areas of hyperinflation and collapse develop, resulting in complex changes in overall pulmonary mechanics. We investigated the effect of measuring resonance frequency of the respiratory system by phase analysis at different points of the respiratory cycle: end of inspiration, end of expiration, mid-inspiration and mid-expiration. Ten ventilated premature infants with respiratory distress syndrome were studied, gestational age ranged from 24 to 30 weeks (mean 27.6 weeks) and birth weight ranged from 0.7 to 1.505 kg (mean 0.984 kg). Results: The resonance frequency was consistently higher when measured at the end of inspiration compared with the end of expiration. The expected trend of phase variation, that is, negative below the resonance frequency and positive above, was most consistently found when analysis was done at the end of inspiration. Conclusions: These findings were most likely a result of the complexity of pulmonary mechanics in the surfactant-deficient lungs, rendering the single compartment model we based our theory on inadequate. However, phase analysis performed at the end of inspiration seemed to produce the most reliable and consistent results. 1998 IPEM. Published by Elsevier Science Ltd. All rights reserved. Keywords: High-frequency oscillation; Neonates; Phase analysis
1. Introduction High-frequency oscillatory ventilation in neonatal practice has become widely advocated over the past 10 years [1,2]. The traditional frequency used for oscillation is 10 Hz. We theorized that potential benefits can be gained by oscillating neonates with the resonance frequency of their respiratory system through achieving more efficient ventilation. The resonance frequency of the respiratory system is defined as the frequency at which elastance and inertance cancel out and should, in theory, be the frequency at which oscillatory ventilation is most efficient [3]. This frequency is remarkably constant at approximately 5–6 Hz for both healthy adults and infants [4,5]. Expanding from the principles of the forced oscillatory techniques for measuring respiratory impedance [6–9], we devised a method using phase analysis to measure the resonance frequency of the respiratory system. Our theory was based on a single com-
* Corresponding author.
partment model, and in order to apply our theory in a clinical setting, we examined the effect of measuring the resonance frequency at various points of the respiratory cycle where the lungs are at different stages of expansion and deflation, in neonates with respiratory distress syndrome. Respiratory distress syndrome was chosen, simply because it is one of the most common conditions leading to respiratory morbidity requiring assisted ventilation in neonatal practice.
2. Theory In an oscillating system, if the respiratory system is modelled as a single compartment, its overall impedance can be regarded as the composite of three components. These are: (1) resistance of the respiratory system, which is mainly due to airway resistance, and is a function of the radius of the airway; (2) elastance, which is the reciprocal of compliance and is a function of the stiffness of the pulmonary tissue and chest wall; (3) inertance, which is largely composed of the force opposing acceler-
1350-4533/98/$19.00 1998 IPEM. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 0 - 4 5 3 3 ( 9 8 ) 0 0 0 4 2 - 3
S. Lee et al. / Medical Engineering & Physics 20 (1998) 452–457
ation of gas in the respiratory system. Unlike resistance, inertance and elastance are reactive components, i.e. their effect is dependent on the frequency of ventilation. It is apparent, therefore, that the overall impedance of the respiratory system changes with the frequency of ventilation [8]. When a driving force is applied to the respiratory system, a gas flow is created. The interaction between this flow and the system impedance generates pressure through the dissipation of energy. As impedance varies with ventilation frequency, the amplitude of the resultant pressure will vary. More importantly, the phase difference between flow and pressure will also vary. The single compartment model was a direct analogy in the classical resonant circuit of electrical AC theory [8,10] (Scheme 1). The voltage, V, developed across a circuit composed of resistance R, capacitance C and inertance L; driven by a current I is given by the formula: V = RI + LdI/dt + 1/C兰Idt
(1)
where = 2f, the angular frequency. In the resistor, V and I are in phase. In the inductor, V leads I by 90° and in the capacitor, V lags I by 90°. Thus the voltages in these two components are 180° out of phase. At the frequency where L = 1/C, the inductive and capacitive terms cancel out, thus resistance is the only impedance to flow and V and I are in phase. By definition, this is the resonance frequency, f0.
L = 1/C⇒0 = √(1/LC)⇒f0 = (1/2)√(1/LC)
(2)
3. Methods and patients High-frequency oscillation was provided by a custombuilt piston-based oscillator that had an oscillating frequency range of 2–30 Hz and a capacity of delivering constant tidal volumes of between 2 and 20 ml, by adjusting a movable fulcrum on the camshaft. A sine– cosine electrical generator connected to the cam of the system produced a sinusoidal electrical signal that represented the changes in piston position. Rotating the sine–cosine generator on its own axis allowed us to alter the phase relationship between the electrical output signal and the piston position if necessary. For the purpose of this study, the output signal was rotated 90° from the original position, thereby aligning it in phase with flow. Mean airway pressure support was provided by a conventional ventilator (either Sechrist Infant ventilator, model IV-100B or SLE 2000 Infant ventilator) on the continuous positive airway pressure mode; with the oscillator connected to the suction port at the patient manifold (Fig. 1). Changes in airway opening pressure were monitored at the proximal end of the endotracheal tube using a Validyne pressure transducer (MP15-20). The frequency response has been tested and over the range of 14–26 Hz, the response was within 7%. The output signal from the oscillator, together with the signal representing the changes of airway opening pressure were recorded via a frequency-modulated tape recorder onto magnetic tape. The signals from the magnetic tape were then sampled at 2000 Hz, using a digital data acquisition card with an anti-alias filtering device. The data was stored on computer hard disk. Phase analyses were performed on four set points of the respiratory
Eq. (1) can be rewritten in terms of the respiratory system as follows: Pmouth = RrsV⬘ + IrsV⬙ + (1/Crs)V
(3)
where Pmouth is mouth pressure; Rrs is resistance; Irs is inertance; Crs is compliance (reciprocal of elastance); V is volume; V⬘ is flow; and V⬙ is the time derivative of flow. Therefore, at the frequency where Irs = 1/Crs, resonance occurs with two important effects: 1. mouth pressure is in phase with flow; 2. the only impedance to flow is resistance, thus ventilation should be more efficient.
Scheme 1.
453
Fig. 1.
Schematic representation of ventilatory circuit.
454
S. Lee et al. / Medical Engineering & Physics 20 (1998) 452–457
cycle; mid-inspiration, end of inspiration, mid-expiration and end of expiration, using a custom-built computer program; by identifying the corresponding points on the two traces (Fig. 2). Ten premature ventilated infants with respiratory distress syndrome were recruited into the study. Gestational age ranged from 24 to 30 weeks (mean 27.6 weeks). Birth weight ranged from 0.7 to 1.505 kg (mean 0.984 kg). Informed written consent was obtained from at least one parent and the study was approved by the Ethics Committee of West Lambeth Health Authority. Each infant was oscillated from 8 to 30 Hz and back down to 8 Hz. This run was repeated to produce a measure of reproducibility. Mean airway pressure used in each case was 2 cmH2O higher than that employed during conventional ventilation. Volume delivery was set at 4 ml in all 10 cases.
4. Results All 10 infants completed the study with no adverse effects. The linear relationship between the phase difference and increasing oscillating frequencies was most consistently seen when phase analysis was performed at the end of inspiration. The expected trend, that is, negative below the resonance frequency and positive above, becoming more positive as frequency increases further was also most consistently observed at this point. We took the resonance frequency in this study as the frequency at which phase difference is closest to zero. The distribution of phase differences with varying oscillating frequencies is demonstrated in graph form in Fig. 3. The general trend of phase difference, that is, negative below the resonance frequency, and positive above, was seen
Fig. 2. A screen from our phase analysis program, showing phase analysis performed at four points of the respiratory cycle: top of breath, mid-inspiration, mid-expiration and bottom of breath. Corresponding points from the driving trace and the mouth pressure trace are matched and the phase difference calculated. In this case, the phase difference at the top of breath is 0° at an oscillating frequency of 20 Hz.
in most of the cases studied. The resonance frequencies found in all 10 infants at the four chosen points of the respiratory cycle are summarized in Table 1. In eight out of 10 cases, the resonance frequency was lowest at the end of expiration. This frequency was consistently higher when measured at the end of inspiration compared with at the end of expiration.
5. Discussion The relationship between resonance frequency, inertance and compliance can be summarized using the following equation [4] (cf. Eq. (2): 2f = 1/√(IC)
(4)
where f is the resonance frequency; I is inertance and C is compliance. At the end of inspiration, when the thoracic gas volume is relatively high, elastance or elastic recoil; the natural tendency for a stretched object to return to the resting, unstretched state is high. Compliance, being the reciprocal of elastance, is therefore low. As a result of a drop in C in the above equation, f increases (see Eq. (4)). The volume of air in the lungs is also at its maximum at the end of inspiration. In theory, this may cause an increase in I and therefore a decrease in f. However, the tidal volume in our premature recruits is extremely small. Consequently, the resultant changes in inertance is also relatively small. As a result, the resonance frequency measured at the end of inspiration is expected to be higher, when elastance is high and the absolute increase in lung volume and therefore inertance, is relatively insignificant; compared with that measured at the end of expiration. It becomes much more difficult to analyse and understand the measurements taken at mid-inspiratory and mid-expiratory points. The single compartment model on which we based our theory is not ideal when dealing with the respiratory system in premature infants with respiratory distress syndrome. In the surfactant-deficient state, the lungs become an inhomogenous complex structure with localized areas of consolidation and hyperinflation. As a result, the reproducibility of measurements at these points becomes unreliable. By definition, flow is in phase with resistance and 90° out of phase with the driving pressure. However after rotating the output signal through 90°, driving pressure becomes in-phase with flow. Below the resonance frequency, the (1/Crs)V component dominates in Eq. (3), where V represents the volume. Therefore, mouth pressure (or the resultant pressure) lags the driving pressure, resulting in a negative phase difference. Above the resonance frequency, the IrsV⬙ component dominates, where V⬙ is the time derivative of flow. Mouth pressure
S. Lee et al. / Medical Engineering & Physics 20 (1998) 452–457
455
Table 1 Summary of resonance frequencies found in all 10 babies (1 and 2 represents first and second run, respectively) Baby
One
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ten
Top 1 Top 2 Bottom 1 Bottom 2 Mid-inspiration 1 Mid-inspiration 2 Mid-expiration 1 Mid-expiration 2
22 22 19 15 21 22 24 24
20 20 17 17 19 19 21 20
16 15 10 9 14 15 19 19
20 19 15 9 20 19 19 17
20 20 9 19 19 20 21 17
17 17 15 14 16 16 18 18
22 22 17 17 20 21 20 20
23 22 19 18 16 16 9 8
17 16 13 13 15 15 17 16
12 12 9 16 9 9 8 14
Fig. 3.
Graphic representation of phase variation in babies 1–10.
now leads driving pressure resulting in a positive phase difference. At resonance frequency, when Irs and Crs cancel out, Pmouth = RrsV⬘, i.e. mouth pressure is in phase with driving pressure or phase difference is zero. In our study, it was not always possible to produce this expected trend of variation in phase difference with changing oscillating frequencies when measurements were done at our four chosen points in the respiratory cycle. Again, this inconsistency is probably due to the complex variation in pulmonary mechanics in the diseased lungs. However, we found that this trend was most consistently found when measurements were performed at the end of inspiration.
6. Conclusion Due to the complexity of the pulmonary mechanics in respiratory distress syndrome, the single compartment model on which we based our theory was not entirely fitting. However, phase analysis performed at the end of inspiration does provide us with the most accurate and reproducible results for the measurement of resonance frequency of the respiratory system. High-frequency oscillatory ventilation (HFOV) at resonance frequency could in theory provide more efficient ventilation compared with the conventional 10 Hz, since by definition, at this frequency, elastance and inertance cancel out.
456
S. Lee et al. / Medical Engineering & Physics 20 (1998) 452–457
Fig. 3.
Elastance is one of the major contributors to difficulty in ventilation in the surfactant-deficient lungs in premature neonates. A reliable method for measuring resonance frequency would certainly help towards designing a clinical trial to compare HFOV at resonance frequency of the respiratory system and at the conventional 10 Hz.
Acknowledgements Financial support for this project was gratefully received from Tommy’s Campaign, UK.
Continued.
References [1] Gertsmann DR, Minton D, Stoddard RA, Meredith KS, Monaco F, Bertrand JM, Batlisti O, Langhendries JP, Francois A, Clark RH. The PROVO Multicentre Early High Frequency Oscillatory Ventilation Trial: improved pulmonary and clinical outcome in respiratory distress syndrome. Pediatrics 1996;98:1044–57. [2] Clark RH, Gertsmann DR, Null DM, DeLemos RA. Prospective randomised comparison of high frequency oscillatory and conventional ventilation in respiratory distress syndrome. Pediatrics 1992;89:5–12. [3] Stocks J, Sly P, Tepper R, Morgan W. Infant respiratory function testing. USA: J. Wiley and Sons, Inc., 1996;8–9. [4] Mead J. Measurement of inertia of lungs at increased ambient pressure. Journal of Applied Physiology 1956;9:208–12.
S. Lee et al. / Medical Engineering & Physics 20 (1998) 452–457
[5] Mead J. Contribution of compliance of airways to frequencydependent behaviour of lungs. Journal of Applied Physiology 1969;5:670–3. [6] Cotes JE. Lung function assessment and application in medicine, 5th ed. Blackwell Scientific Publications, 1993;169–71. [7] Von Gierke HE, Oestriecher HL, Franke EK, Parrack HO, Von Wittern WW. Physics of vibrations in living tissues. Journal of Applied Physiology 1952;4:886–900. [8] DuBois AB, Brody AW, Lewis DH, Franklin Bergess JR. Oscil-
457
lation mechanics of lungs and chest in man. Journal of Applied Physiology 1956;8:587–94. [9] Zwart A, Peslin R. Mechanical respiratory impedance: the forced oscillatory method. Contributions to the workshop held for the European Commission on 18–19 June 1990, Antwerp, Belgium. European Respiration 1991;RevI:131–237. [10] Suprynowicz V. Introduction to electronics. USA: Addison–Wesley Publishing Company, 1966:91–3.