Respiration .?«: 327-331 (1979)
A Simple Method for Computing Airway Resistance and Specific Airways Conductance from Scalar Plethysmographie Recordings' M. Derron and H. Bachofen Department of Medicine, University of Berne, Inselspital, Berne
Key Words. Airways resistance • Specific airway conductance • Body plethysmography
Introduction Inhomogenous ventilation of different parts of the lung is usually the source of a phase shift between ‘mean’ alveolar pres sure and airflow measured at the mouth: ac cordingly, the plethysmographically regis tered alveolar pressure (PA) versus airflow (V) diagram forms a loop [3, 6, 10-12], such that an unequivocal slope of the PA—V relationship cannot be drawn for the assessment of airway resistance (Raw). This difficulty can be overcome by mea suring the flow resistive component of the 1 Supported by the Swiss National Science Foun dation, grant No. 3.731.72.
work of breathing, and by computing Raw averaged over one breathing cycle. On the basis of this principle several methods have been worked out which yield significant and comparable results [5, 7, 9, 13]. The price, however, is a more time-consuming compu tation of the data, or a more involving tech nique eventually requiring a computer sys tem [5, 11]. An alternative procedure, which offers two advantages is presented in this report: (1) mean Raw and mean specific airway conductance (SGaw) can be obtained with modest technical equipment, and with mini mal work expense, and (2) SGaw can be di rectly obtained without measuring the intra thoracic gas volume.
Downloaded by: King's College London 137.73.144.138 - 3/7/2018 11:42:50 PM
Abstract. An alternative procedure to evaluate plethysmographic tracings is described for the determination of airway resistance (Raw) and specific airway conductance (SGaw). Raw and SGaw obtained with this method reflect the average resistive impedance over one breathing cycle. Although both work and apparative expenditures are minimal, the results are well comparable with those calculated with more involved methods. The technique is particularly well suited for patients with impaired cooperation since SGaw can be determined without measuring the intrathoracic gas volume.
Derron/Bachofen
328
Methods Apparatus A volume displacement plcthysmograph was used for all measurements [1, 8], A sensitive ther mostabilizer within the rebreathing system adjust ed the temperature of the fully humified inspriatory gas to + 0 .1 C of the patients’ body tempera ture [6|. A large Fleisch pneumotachograph (No. 4) connected mouthpiece and airconditioner. All variables - airflow at the mouth (V ), tidal volume (V-r), mouth pressure, and the volume variations of the body box (Vb) - were plotted si multaneously on photographic paper by a multi channel recorder (DR8, Electronics for Medicine). Evaluation of the Recordings The theoretical considerations and mathemati cal derivations are given in detail in the ‘Appen
dix': with the given formulations the use of a vol ume displacement plethysmograph is envisaged. Accordingly, two measurement variables only, i.e., the spirogram (Vt ) and the volume fluctuations of the plcthysmograph (Vb) have to be recorded for the computation of specific airway conductance (formula 8 in ‘Appendix’): Vt • (tl + tE)
SGaw = k' •
(Pis - Pirn) - (tE • AI + tl • AE) where tl and tE denote the inspiratory and expira tory time intervals (expressed in seconds), respec tively, Vt is the tidal volume of the breathing cy cle considered, and AI and AE are areas engulfed by the Vb curve. As shown in figure 1, these areas can easily be measured by planimetry after having connected the end-inspiratory and end-expiratory points, k' takes into account the calibration fac tors.
Table I. Airway resistances (Raw, cm l+O/l/sec) computed with four different methods (A-D) f
VT
Raw A VaréneJacquemin
B Scalar method
C JaegerOtis
D NisellEhrner
H. R. (normal)
19 29 39 59
1.12 1.04 1.06 1.02
1.73 2.03 1.69 1.90
1.56 2.00 1.64 1.85
1.49 1.88 1.47 1.65
1.49 1.88 1.47 1.65
F.B. (emphysema)
18 28 40 58
1.06 1.04 0.97 1.00
1.93 1.93 2.46 3.64
1.97 1.88 2.41 3.73
1.73 1.72 2.15 3.30
1.68 1.70 2.13 3.26
L. A. (bronchial asthma)
18 30 39 50
0.95 0.99 0.90 0.90
5.74 5.90 9.81 8.82
5.75 5.86 9.61 9.65
5.89 5.42 8.77 7.83
5.77 5.26 8.74 7.69
F. M. (fibrosing alveolitis)
19 29 40 60
1.00 1.20 1.28 1.16
2.05 1.70 2.11 2.01
2.15 1.62 2.05 1.90
2.04 1.75 2.02 1.72
2.02 1.62 2.00 1.72
f = Respiratory frequency (breaths/min); Vt = tidal volume (liters).
Downloaded by: King's College London 137.73.144.138 - 3/7/2018 11:42:50 PM
Patients
329
Measurement of Specific Airway conductance
Table II. Differences and their statistical signifi cance between the results (listed in table I) computed by different methods Method of computation
Mean absolute Paired dilferences differences in % from method A of values of A (mean ± SD)
B Scalar method 2.9
-0.06 ± 0.09 (p ' 0.025)
C Jaeger-Otis
-0.29 ± 0.32 (0.001 p 0.005)
8.9
D Nisell-Ehrner 9.6
As.ies.wiem of Accuracy Using the apparatus described above, measure ments have been performed in 4 persons (1 healthy subject, 1 patient with emphysema. 1 pa tient with bronchial asthma, and 1 with fibrosing alveolitis) at four different frequencies of brea thing. All recordings have been evaluated with the proposed ‘scalar’ method, and with the well-esta blished methods of Varène and Jacquemin [131, Jaeger and Otis [7], and Nisell and Ehrner [91. The results obtained with the method of Varène and Jacquemin have been chosen as reference, since this method allows one to compute mean Raw, or mean SGaw with a minimum of assump tions. For statistical analysis paired observations have been compared using the t test |4|.
Results All results have been expressed in terms of 'mean’ Raw for the sake of clarity, and are listed in table I. Evidently, the differ ences between the results obtained by differ ent methods are rather small. There is an excellent agreement between the proposed scalar method and the reference method of Varène and Jacquemin [13]. On the other
hand, Raw calculated with the methods of Jaeger and Otis [7] or of Nisell and Ehrner [9], respectively, are on average about 10°/o lower. Absolute and relative values of the differences, and their statistical significance are given in table II.
Discussion The proposed method to compute Raw and SGaw can be criticized on three points. (1) In its present form the method seems ex clusively to apply to recordings obtained by a volume displacement plethysmograph. However, with only minor modifications the recordings of a plethysmograph of the type designed by DuBois et al. [3] can be evalu ated in a likewise manner. (2) The need for planimetry might be considered old-fash ioned and irksome. Indeed, an automatic handling of the recordings by a small com puter, or microprocessor is well feasible. The entire evaluation of the registered curves takes less than 5 min (including the work of planimetry): depending on the task this work expense has to be weighed with
Downloaded by: King's College London 137.73.144.138 - 3/7/2018 11:42:50 PM
Fig. 1. Tidal volume (Vt ) and body box varia tion during one breathing cycle. The stippled areas are measured by planimetry. For further explana tion see text.
-0.34 ± 0.34 ( p ^ 0.001)
330
Appendix Airway resistance averaged over one breathing cycle can be expressed by the ratio of the area of the pressure-volume loop to the area of the corresponding flow-volume loop [13], Raw
j P a ■dV (I)
f V- dV Using a volume displacement piethysmograph alveolar pressure (Pa) has to be calculated from the box volume variations (Vb), the intrathoracic gas volume (Vi,), and the barometric pressure reduced by the water vapor pressure (Pb - P h >o). Hence P a = P l l ~ P — -Vb.
V,. and P b —P h 20 4'Vb dV Raw = ----------- ------------- . Vj. j'V -dV
(2)
Change of variables and rearrangement of the numera tor yield: tl dv U+tE dv f Vb dV = / Vb(t)------dt + J Vb(t) •— • dt, (3) o dt tl dt where tl and tE denote the durations of inspiration and expiration, respectively. Applying the theorem of mean value: I tl tl ( Vb dV = — f Vdt J Vb(t) dt + d o o l tl-f-tE tl 4-tE — • jV dtJV b(t)dt. (E ti ti tl tl + tE On the assumption that J Vdt = J Vdt = Vt o tl
(4)
(Vt denotes the tidal volume) one may rearrange: VT 11 tl+tE § Vb • dV ----------(tE • J Vb(t)dt + 11-/ Vb(t)dt). (5) tl • tE o tl The denominator of equation 2 can be handled in a similar manner: V(tl)
V(tl + tE)
f VdV = J VdV + J VdV V(t=0) V(tl)
Downloaded by: King's College London 137.73.144.138 - 3/7/2018 11:42:50 PM
that required for the maintenance of extra hardware before allocating a substantial amount of money for the acquisition of a re liable, digitalized system. (3) But most im portant of all, by linearly interpolating the baseline of the Vb curve between end-in spiratory and end-expiratory points (where airflow at the mouth is zero) a questionable approximation is made. In fact, the exact course of this baseline required for planime try is indeterminable. However, the very close agreement of the results obtained with this method and that of Varene and Jacquemin [13] indicates that possibly bidirec tional deviations of the "true’ baseline from the interpolated straight line are either small or cancel out. As mentioned before, the feasibility to accurately and rapidly determine Raw and SGaw with minimal apparative require ments is one advantage of the method: an inexpensive two-channel recorder is an ade quate recording system which is well within the financial reach of smaller laboratories and clinical units with tighter budgets. In addition, the procedure enables one to di rectly measure SGaw in disabled and noncooperative patients. By experience, a ma jor source of error of Raw and SGaw mea surements is bound to the determination of intrathoracic gas volume owing either to technical factors [2], or to the awkwardness of patients to 'breathe’ properly against a closed valve. Using formula 8 to compute SGaw one requires the registration of the spirogram and the volume changes of the piethysmograph during spontaneous brea thing only, and hence SGaw can be mea sured easily in disabled elderly patients as well as in small children provided that they can be accommodated in the body box, and that they are able to breathe spontaneously through a mouthpiece.
Derron/Bachofen
Measurement of Specific Airway conductance
tl+tE
= f V123d t + J V2dt O
ti
I
4
ti
j
tl + iE
= - • ( / Vdt)2 + — • (/ Vdt)2 tl o tE ti
5
and with the same assumption as in equation 5 , .
tl+tE
( 6)
4 V d V = V2t -------------
tl • tE
6
Thus, Raw can be computed by the ratio of equations 5 and 6: ll
tl + tE
7
tE • f Vb(t)dt + tl f Vb(t)dt Raw
Pr - P
h 2o
_____________ ti________
Vi,
Vt •(tl + tE)
P r - P h2o tE • AI + tl • AE = k --------------------------------------------(7) Vi.
8
V i d l + tE)
The numerical value of both integrals (AI and AE) can be obtained by planimetry of the Vb tracings: all other variables are easily measurable (k takes into account the different calibration factors). The specific airway conductance, i.e., the reciprocal value of Raw divided by Vi., can be directly obtained without the determination of intrathoracic gas volume: VT - (tl + tE)
SG aw = k ' •
(
(P r - P
h 2o)
8)
9
10
11
- (tE • AI + tl - AE)
References 1 Bachofen, H.: Die mechanischen Eigenschaften der Lunge (Huber, Bern 1969). 2 Brown, R.; Hoppin, F. G., Jr.; Ingram, R. H., Jr.) Saunders, N. A., and McFadden, E. R., Jr.: Influence of abdominal gas on the Boyle’s law determination of thoracic gas volume. J. appl. Physiol. 44: 469-473 (1978). 3 DuBois, A. B.; Botelho, S. Y., and Comroe, J. H„ Jr.: A new method for measuring airway resistance in man using a body plethysmograph. Values in normal subjects and in pa-
12
13
tients with respiratory disease. J. clin. Invest. 35: 327-335 (1956). Goldstein, A.: Biostatistics (MacMillan, New York 1969). Hantos, Z.; Galgoczy, G.; Davoczy, B., and Dambos, K.: Computation of the equivalent airway resistance: a comparison with routine evaluations of plcthysmographic measure ments. Respiration 36: 64-72 (1978). Jaeger, M. J. and Bouhuys, A.: Loop forma tion in pressure vs. flow diagrams obtained by body plethysmographic techniques. Body pleth ysmography. Progr. Resp. Res., vol. 4, pp. 116-130 (Karger, Basel 1969). Jaeger. M. J. and Otis, A. B.: Measurement of airway resistance with a volume displacement plethysmograph. J. appl. Physiol. 19: 813-820 (1964). Mead, J.: Volume displacement plethysmo graph for respiratory measurements in human subjects. J. appl. Physiol. 15: 736-740 (1960). Nisell. O. and Ehrner, L.: The resistance to breathing determined from time-marked respi ratory pressure-volume loops. Acta med. scand. 161: 427-436 (1958). Nitta, K. and Mochizuki, M.: Study of the time displacement between the airflow and the box pressure curves in the body plethysmo graph. Med. biol. Engng 5: 481-487 (1967). Smidt, U.; Finkenzeller, P. und Rennings, C.: On-line Computereinsatz in der Ganzkorperplethysmographie zur Berechnung der mittleren Resistance. Pncumologie 151: 223-231 (1975). Ulmer, W. T.; Reif, E. und Weller, W.: Die obstruktiven Atennvegserkrankungen (Thieme. Stuttgart 1969). Varene, P. and Jacquemin, C.: Airways resist ance; in Bouhuys, Airway dynamics (Thomas, Springfield 1970).
Received: March 20, 1979 Accepted: July 17, 1979 H. Bachofen, Department of Medicine, University of Berne, Inselspital, CH-3010 Berne (Switzerland)
Downloaded by: King's College London 137.73.144.138 - 3/7/2018 11:42:50 PM
ti
331
A Simple Method for Computing Airway Resistance and Specific Airways Conductance from Scalar Plethysmographie Recordings' M. Derron and H. Bachofen Department of Medicine, University of Berne, Inselspital, Berne
Key Words. Airways resistance • Specific airway conductance • Body plethysmography
Introduction Inhomogenous ventilation of different parts of the lung is usually the source of a phase shift between ‘mean’ alveolar pres sure and airflow measured at the mouth: ac cordingly, the plethysmographically regis tered alveolar pressure (PA) versus airflow (V) diagram forms a loop [3, 6, 10-12], such that an unequivocal slope of the PA—V relationship cannot be drawn for the assessment of airway resistance (Raw). This difficulty can be overcome by mea suring the flow resistive component of the 1 Supported by the Swiss National Science Foun dation, grant No. 3.731.72.
work of breathing, and by computing Raw averaged over one breathing cycle. On the basis of this principle several methods have been worked out which yield significant and comparable results [5, 7, 9, 13]. The price, however, is a more time-consuming compu tation of the data, or a more involving tech nique eventually requiring a computer sys tem [5, 11]. An alternative procedure, which offers two advantages is presented in this report: (1) mean Raw and mean specific airway conductance (SGaw) can be obtained with modest technical equipment, and with mini mal work expense, and (2) SGaw can be di rectly obtained without measuring the intra thoracic gas volume.
Downloaded by: King's College London 137.73.144.138 - 3/7/2018 11:42:50 PM
Abstract. An alternative procedure to evaluate plethysmographic tracings is described for the determination of airway resistance (Raw) and specific airway conductance (SGaw). Raw and SGaw obtained with this method reflect the average resistive impedance over one breathing cycle. Although both work and apparative expenditures are minimal, the results are well comparable with those calculated with more involved methods. The technique is particularly well suited for patients with impaired cooperation since SGaw can be determined without measuring the intrathoracic gas volume.
Derron/Bachofen
328
Methods Apparatus A volume displacement plcthysmograph was used for all measurements [1, 8], A sensitive ther mostabilizer within the rebreathing system adjust ed the temperature of the fully humified inspriatory gas to + 0 .1 C of the patients’ body tempera ture [6|. A large Fleisch pneumotachograph (No. 4) connected mouthpiece and airconditioner. All variables - airflow at the mouth (V ), tidal volume (V-r), mouth pressure, and the volume variations of the body box (Vb) - were plotted si multaneously on photographic paper by a multi channel recorder (DR8, Electronics for Medicine). Evaluation of the Recordings The theoretical considerations and mathemati cal derivations are given in detail in the ‘Appen
dix': with the given formulations the use of a vol ume displacement plethysmograph is envisaged. Accordingly, two measurement variables only, i.e., the spirogram (Vt ) and the volume fluctuations of the plcthysmograph (Vb) have to be recorded for the computation of specific airway conductance (formula 8 in ‘Appendix’): Vt • (tl + tE)
SGaw = k' •
(Pis - Pirn) - (tE • AI + tl • AE) where tl and tE denote the inspiratory and expira tory time intervals (expressed in seconds), respec tively, Vt is the tidal volume of the breathing cy cle considered, and AI and AE are areas engulfed by the Vb curve. As shown in figure 1, these areas can easily be measured by planimetry after having connected the end-inspiratory and end-expiratory points, k' takes into account the calibration fac tors.
Table I. Airway resistances (Raw, cm l+O/l/sec) computed with four different methods (A-D) f
VT
Raw A VaréneJacquemin
B Scalar method
C JaegerOtis
D NisellEhrner
H. R. (normal)
19 29 39 59
1.12 1.04 1.06 1.02
1.73 2.03 1.69 1.90
1.56 2.00 1.64 1.85
1.49 1.88 1.47 1.65
1.49 1.88 1.47 1.65
F.B. (emphysema)
18 28 40 58
1.06 1.04 0.97 1.00
1.93 1.93 2.46 3.64
1.97 1.88 2.41 3.73
1.73 1.72 2.15 3.30
1.68 1.70 2.13 3.26
L. A. (bronchial asthma)
18 30 39 50
0.95 0.99 0.90 0.90
5.74 5.90 9.81 8.82
5.75 5.86 9.61 9.65
5.89 5.42 8.77 7.83
5.77 5.26 8.74 7.69
F. M. (fibrosing alveolitis)
19 29 40 60
1.00 1.20 1.28 1.16
2.05 1.70 2.11 2.01
2.15 1.62 2.05 1.90
2.04 1.75 2.02 1.72
2.02 1.62 2.00 1.72
f = Respiratory frequency (breaths/min); Vt = tidal volume (liters).
Downloaded by: King's College London 137.73.144.138 - 3/7/2018 11:42:50 PM
Patients
329
Measurement of Specific Airway conductance
Table II. Differences and their statistical signifi cance between the results (listed in table I) computed by different methods Method of computation
Mean absolute Paired dilferences differences in % from method A of values of A (mean ± SD)
B Scalar method 2.9
-0.06 ± 0.09 (p ' 0.025)
C Jaeger-Otis
-0.29 ± 0.32 (0.001 p 0.005)
8.9
D Nisell-Ehrner 9.6
As.ies.wiem of Accuracy Using the apparatus described above, measure ments have been performed in 4 persons (1 healthy subject, 1 patient with emphysema. 1 pa tient with bronchial asthma, and 1 with fibrosing alveolitis) at four different frequencies of brea thing. All recordings have been evaluated with the proposed ‘scalar’ method, and with the well-esta blished methods of Varène and Jacquemin [131, Jaeger and Otis [7], and Nisell and Ehrner [91. The results obtained with the method of Varène and Jacquemin have been chosen as reference, since this method allows one to compute mean Raw, or mean SGaw with a minimum of assump tions. For statistical analysis paired observations have been compared using the t test |4|.
Results All results have been expressed in terms of 'mean’ Raw for the sake of clarity, and are listed in table I. Evidently, the differ ences between the results obtained by differ ent methods are rather small. There is an excellent agreement between the proposed scalar method and the reference method of Varène and Jacquemin [13]. On the other
hand, Raw calculated with the methods of Jaeger and Otis [7] or of Nisell and Ehrner [9], respectively, are on average about 10°/o lower. Absolute and relative values of the differences, and their statistical significance are given in table II.
Discussion The proposed method to compute Raw and SGaw can be criticized on three points. (1) In its present form the method seems ex clusively to apply to recordings obtained by a volume displacement plethysmograph. However, with only minor modifications the recordings of a plethysmograph of the type designed by DuBois et al. [3] can be evalu ated in a likewise manner. (2) The need for planimetry might be considered old-fash ioned and irksome. Indeed, an automatic handling of the recordings by a small com puter, or microprocessor is well feasible. The entire evaluation of the registered curves takes less than 5 min (including the work of planimetry): depending on the task this work expense has to be weighed with
Downloaded by: King's College London 137.73.144.138 - 3/7/2018 11:42:50 PM
Fig. 1. Tidal volume (Vt ) and body box varia tion during one breathing cycle. The stippled areas are measured by planimetry. For further explana tion see text.
-0.34 ± 0.34 ( p ^ 0.001)
330
Appendix Airway resistance averaged over one breathing cycle can be expressed by the ratio of the area of the pressure-volume loop to the area of the corresponding flow-volume loop [13], Raw
j P a ■dV (I)
f V- dV Using a volume displacement piethysmograph alveolar pressure (Pa) has to be calculated from the box volume variations (Vb), the intrathoracic gas volume (Vi,), and the barometric pressure reduced by the water vapor pressure (Pb - P h >o). Hence P a = P l l ~ P — -Vb.
V,. and P b —P h 20 4'Vb dV Raw = ----------- ------------- . Vj. j'V -dV
(2)
Change of variables and rearrangement of the numera tor yield: tl dv U+tE dv f Vb dV = / Vb(t)------dt + J Vb(t) •— • dt, (3) o dt tl dt where tl and tE denote the durations of inspiration and expiration, respectively. Applying the theorem of mean value: I tl tl ( Vb dV = — f Vdt J Vb(t) dt + d o o l tl-f-tE tl 4-tE — • jV dtJV b(t)dt. (E ti ti tl tl + tE On the assumption that J Vdt = J Vdt = Vt o tl
(4)
(Vt denotes the tidal volume) one may rearrange: VT 11 tl+tE § Vb • dV ----------(tE • J Vb(t)dt + 11-/ Vb(t)dt). (5) tl • tE o tl The denominator of equation 2 can be handled in a similar manner: V(tl)
V(tl + tE)
f VdV = J VdV + J VdV V(t=0) V(tl)
Downloaded by: King's College London 137.73.144.138 - 3/7/2018 11:42:50 PM
that required for the maintenance of extra hardware before allocating a substantial amount of money for the acquisition of a re liable, digitalized system. (3) But most im portant of all, by linearly interpolating the baseline of the Vb curve between end-in spiratory and end-expiratory points (where airflow at the mouth is zero) a questionable approximation is made. In fact, the exact course of this baseline required for planime try is indeterminable. However, the very close agreement of the results obtained with this method and that of Varene and Jacquemin [13] indicates that possibly bidirec tional deviations of the "true’ baseline from the interpolated straight line are either small or cancel out. As mentioned before, the feasibility to accurately and rapidly determine Raw and SGaw with minimal apparative require ments is one advantage of the method: an inexpensive two-channel recorder is an ade quate recording system which is well within the financial reach of smaller laboratories and clinical units with tighter budgets. In addition, the procedure enables one to di rectly measure SGaw in disabled and noncooperative patients. By experience, a ma jor source of error of Raw and SGaw mea surements is bound to the determination of intrathoracic gas volume owing either to technical factors [2], or to the awkwardness of patients to 'breathe’ properly against a closed valve. Using formula 8 to compute SGaw one requires the registration of the spirogram and the volume changes of the piethysmograph during spontaneous brea thing only, and hence SGaw can be mea sured easily in disabled elderly patients as well as in small children provided that they can be accommodated in the body box, and that they are able to breathe spontaneously through a mouthpiece.
Derron/Bachofen
Measurement of Specific Airway conductance
tl+tE
= f V123d t + J V2dt O
ti
I
4
ti
j
tl + iE
= - • ( / Vdt)2 + — • (/ Vdt)2 tl o tE ti
5
and with the same assumption as in equation 5 , .
tl+tE
( 6)
4 V d V = V2t -------------
tl • tE
6
Thus, Raw can be computed by the ratio of equations 5 and 6: ll
tl + tE
7
tE • f Vb(t)dt + tl f Vb(t)dt Raw
Pr - P
h 2o
_____________ ti________
Vi,
Vt •(tl + tE)
P r - P h2o tE • AI + tl • AE = k --------------------------------------------(7) Vi.
8
V i d l + tE)
The numerical value of both integrals (AI and AE) can be obtained by planimetry of the Vb tracings: all other variables are easily measurable (k takes into account the different calibration factors). The specific airway conductance, i.e., the reciprocal value of Raw divided by Vi., can be directly obtained without the determination of intrathoracic gas volume: VT - (tl + tE)
SG aw = k ' •
(
(P r - P
h 2o)
8)
9
10
11
- (tE • AI + tl - AE)
References 1 Bachofen, H.: Die mechanischen Eigenschaften der Lunge (Huber, Bern 1969). 2 Brown, R.; Hoppin, F. G., Jr.; Ingram, R. H., Jr.) Saunders, N. A., and McFadden, E. R., Jr.: Influence of abdominal gas on the Boyle’s law determination of thoracic gas volume. J. appl. Physiol. 44: 469-473 (1978). 3 DuBois, A. B.; Botelho, S. Y., and Comroe, J. H„ Jr.: A new method for measuring airway resistance in man using a body plethysmograph. Values in normal subjects and in pa-
12
13
tients with respiratory disease. J. clin. Invest. 35: 327-335 (1956). Goldstein, A.: Biostatistics (MacMillan, New York 1969). Hantos, Z.; Galgoczy, G.; Davoczy, B., and Dambos, K.: Computation of the equivalent airway resistance: a comparison with routine evaluations of plcthysmographic measure ments. Respiration 36: 64-72 (1978). Jaeger, M. J. and Bouhuys, A.: Loop forma tion in pressure vs. flow diagrams obtained by body plethysmographic techniques. Body pleth ysmography. Progr. Resp. Res., vol. 4, pp. 116-130 (Karger, Basel 1969). Jaeger. M. J. and Otis, A. B.: Measurement of airway resistance with a volume displacement plethysmograph. J. appl. Physiol. 19: 813-820 (1964). Mead, J.: Volume displacement plethysmo graph for respiratory measurements in human subjects. J. appl. Physiol. 15: 736-740 (1960). Nisell. O. and Ehrner, L.: The resistance to breathing determined from time-marked respi ratory pressure-volume loops. Acta med. scand. 161: 427-436 (1958). Nitta, K. and Mochizuki, M.: Study of the time displacement between the airflow and the box pressure curves in the body plethysmo graph. Med. biol. Engng 5: 481-487 (1967). Smidt, U.; Finkenzeller, P. und Rennings, C.: On-line Computereinsatz in der Ganzkorperplethysmographie zur Berechnung der mittleren Resistance. Pncumologie 151: 223-231 (1975). Ulmer, W. T.; Reif, E. und Weller, W.: Die obstruktiven Atennvegserkrankungen (Thieme. Stuttgart 1969). Varene, P. and Jacquemin, C.: Airways resist ance; in Bouhuys, Airway dynamics (Thomas, Springfield 1970).
Received: March 20, 1979 Accepted: July 17, 1979 H. Bachofen, Department of Medicine, University of Berne, Inselspital, CH-3010 Berne (Switzerland)
Downloaded by: King's College London 137.73.144.138 - 3/7/2018 11:42:50 PM
ti
331
