JOURNAL
OF SURGICAL
RESEARCH
18,
571-586 (1975)
Pulmonary Atrial
Septal
Vascular Defect
Response
Closure
to
in Children
1
CAROL L. LUCAS, PH.D., BENSON R. WILCOX, M.D., AND NORMAN A. COULTER, JR., M.D. Division of Cardiothoracic Surgery, University of North Carolina School of Medicine, Chapel Hill, North Carolina 27514 Submitted for publication July 20, 1974
Pulmonary vascular disease increases the risk in performing corrective surgery in patients with heart disease; therefore, reliable techniques for determining the extent of the pulmonary vascular impairment have been sought [g-10, 161.Identification of the hemodynamic factors responsible for the pathogenesisof the diseaseshould also aid in evaluating the status of the patient’s pulmonary vasculature; hence, studies have been done which sought to demonstrate correlation between abnormal pulmonary vasculature development with abnormal hemodynamic variables [ 1l-141. Studies previously done in this laboratory indicate that pulsatile pressure and flow parameters may prove more helpful than the mean pressure and flow values in studying pulmonary hemodynamics [15, 25, 26). The purpose of this investigation was to examine pulmonary vascular dynamics in good surgical risk children before and after atria1 septal defect closure in order to: (1) establish normative values for several impedance-related parameters for this patient population, and (2) understand better the immediate response of the pulmonary vasculature to corrective surgery. A three-segment transmission line model of the pulmonary circulation was used to interpret changes observed in the pulmonary input impedance spectrum as a result of defect correction. ‘Supported by USPHS Grant HL-I 1919-06and NIH Fellowship 4 FOl GM46707-03 STAT.
METHODS Patient Material and Data Acquisition
Pressure and flow data were obtained from six children at the time of atria1 septal defect closure. No patients with endocardial cushion defects or other congenital heart diseases were included. Table 1 lists the patient’s diagnosis, age, sex, and body surface area at the time of operation, as well as the pulmonary arterial pressures and pulmonary-to-systemic blood flow ratios measured at preoperative cardiac catheterization. With the patient under general anesthesia (halothane or fluroxene and oxygen), the heart was exposed through a median sternotomy. The main pulmonary artery was isolated and a flow probe2 of appropriate size was positioned to measure pulsatile blood flow. The amplitude response of the flow probe was flat at 10 Hz and showed less than 2.5% error at 15 Hz; the phase response showed a flat 7 msec time lag, or a linear phase shift of 2.52”/Hz, up to 20 Hz. Pressures were measured through 2-in. 20gauge needles attached by 72-in. large-bore (i.d. 3 mm) saline-filled catheters to a Statham differential manometer (Model ~23H).~ Connections were made so that the right superior pulmonary venous pressure was *Carolina Medical Electronic SquareWave Electromagnetic Flowmeter, Model 321, Series 500 flow probes. King, NC. sStatham Medical Instruments, Inc., Los Angeles, CA.
571 Copyright @1975by Academic Press, Inc. All rights of reproduction in any form reserved.
572
JOURNAL OF SURGICAL RESEARCH VOL. 18, NO. 6, JUNE 1975 TABLE 1 PreoperativeData
ilarly shaped pulses were selected for further processing. Only pulses not obviously showPatient Age,’ PA,b ing the effects of respiration, e.g., the raised No. sex BSA’ Qp/Qsb PA(S/D)b (mm Hg) baseline of the pulmonary artery pressure pulse, were chosen. A pattern recognition 1 4F .69 3.60 48116 26 .84 24104 15 2 SM 1.70 procedure was used to filter the signal and 3 6F .80 2.40 23105 12 remove spikelike artifacts. An autocorrela4 25/08 1.5 6M .79 1.90 tion procedure then determined the exact 5 3M .85 1.60 32108 16 beginning and ending points of each of the n 23109 14 9M .92 1.30 6 pulses and the selected curves over the re‘Age and body surfacearea(BSA) at operation. bFlow ratio (Qp/Qs) and pulmonary artery systolic, fined period of observation, 7, were disdiastolic, and meanpressureat cardiaccatheterization. played on the scope to determine the success of spike removal and selection procedures. recorded directly as well as being automatically subtracted from the pressure measured Fourier Analysis in the main pulmonary artery distal to the Fourier analyses of 10n harmonics were flow probe. The amplitude response of the then performed upon pressure and flow pressure-sensingsystem was flat at 5 Hz and waveforms, giving showed a 40% increase in sensitivity at 10 IOII Hz; the natural frequency was approximately P = PO + c P,sin(kwt + &) (1) 20 Hz. Flow and pressure signals were rek-l corded on magnetic tape for later computer IOII analysis. These measurements were made (2) prior to defect closure and before cannulak-l tion was performed. Postclosure values were where P = pressure; PO = mean pressure; recorded only after cannulae were removed Pk = amplitude of Kth pressure harmonic; and patient was judged to be stable hemodk = phase of Kth pressure harmonic; w = dynamically. Thus, each patient served as 27r/7; Q = flow; Q, = mean flow; Qk = amhis own control in that all data analysis plitude of Kth flow harmonic; qk = phase of was carried out in terms of change in preKth flow harmonic. closure versus postclosure measurements. The information obtained from the analyData Selection seswas used for computing all other paramThe initial step in handling of data was eters, and no other smoothing technique was the selection of analog data collected during employed. The Fourier coefficients and operation; specifically, (1) pulsatile pul- phase angles, the impedance and power monary blood flow, (2) pulmonary input spectrum values, and other key parameters pressure, (3) pulmonary differential pressure, (e.g., pressures and flow, resistance values, and (4) pulmonary venous pressure. A gen- cardiac output, etc.) were then printed as
Q= Qo+c Qksi@t+ *,),
eral purpose
program
sampled all
taped
channels simultaneously. Utilizing a Raytheon analog to digital converter equipped with a Tektronix 611 oscilloscope,5 the data were analyzed and stored in integer form on the disk of an IBM 1130digital computer. Sections of data consisting of n(2-4) sim‘ComputerHardware,Inc., Sacramento,CA. JTektronix,Inc., Seattle,WA.
well as stored on statistical
retrieval
and
master patient file disks. External Work The average power of the pressure and flow waves generated by the right heart (w) was computed as the sum of a mean (M) and an oscillatory (0) component, i.e.,
W=M+O,
LUCAS, WILCOX AND COULTER: ATRIAL
573
SEPTAL DEFECT CLOSURE
aging selected points from all the data sets for each harmonic. A point was included in IOIl the average if the flow modulus was greater 0 = + c PkQkcos(qbp - ‘I’,). (3) than 3 ml/set and the pressure modulus k-l The total external work of the right heart was greater than .4 mm Hg. Standard deviaper minute (TEWR) could then also be tions at each frequency were small when divided into mean (MEWR) and oscillatory these criteria were met. (OEWR) components: RESULTS Values for pulmonary blood flow and TEWR = MEWR + OEWR, mean arterial, venous, and differential preswhere MEWR = 60 M, OEWR = 60 0. (4) sures measured in the operating room are It should be noted that this is an approxi- given in Table 2. Pulmonary blood flow demate measure of external work since it does creased by at least 44% for each patient, not include kinetic energy, considered negli- with the average flow decreasing from 11.54 liters per minute to 4.68 liters per minute gible under these conditions. (P = 0.008) after closure. Mean pulmonary Impedance Spectrum artery and pulmonary vein pressures reThe pulmonary vascular input impedance mained relatively unchanged. The average of spectrum was calculated for each section of the pulmonary artery mean pressures dedata processed. The impedance of the Kth creased from 17.9 mm Hg to 17.7 mm Hg harmonic was (P = 0.951) after closure while mean pulmonary vein pressure rose from 8.3 mm Hg Z(h) = ) Z, ) ejek, (5) to 10.2 mm Hg (P = 0.563) after closure. where 1Zk ) = P,/Q, = modulus and f& = However, both pressures decreased in four & - \k, = phase. patients and markedly increased in two patients (patients 1 and 3). Differential pressure Only harmonics which were multiples of the decreasedor remained relatively unchanged heart rate were considered since intermediate for all patients, the average value decreasing harmonics usually had pressure or flow am- from 9.9 to 8.3 mm Hg (P = 0.185). plitudes within the noise range of the instruValues for input, terminal, and differenmentation. Representative impedance spec- tial resistances are given in Table 3. All tra for each patient both before and after resistance values rose with the exception of defect correction were constructed by aver- differential resistance in patient 2. Input where M = P,,Q,,
TABLE 2 Mean Pressure and Flow before and after Defect Closure
Qm
Patient
(liters/min)
P*m
(mmHg)
pvm
(mmHg)
APItl
(mmHg)
No.
Before
After
Before
After
Before
After
Before
After
1 2 3 4 5 6 Mean
7.45 17.83 8.74 6.64 17.37 11.22 11.54
2.51 8.31 4.44 3.71 4.27 4.83 4.68
19.3 15.4 20.9 17.1 16.2 19.1 17.9
27.0 8.0 28.1 15.7 13.6 13.7 17.7
6.8 7.4 9.7 12.0 8.0 5.7 8.3
14.9 4.9 24.2 10.3 3.7 3.2 10.2
12.7 7.8 10.2 7.3 9.5 11.6 9.9
14.8 2.6 7.3 6.4 9.2 9.5 8.3
P=
.008
,951
.563
.185
Q, = pulmonary blood flow; PA, = pulmonary artery mean pressure;PVm = pulmonary vein mean pressure; AP, = differential pulmonary vascular pressure; P = paired t test, 2 tailed.
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TABLE 3 Vascular Resistance before and after Defect Closure’ PAVRu (dyne-set-cm-s)
PWRo (dyne-see-c&)
PVRn (dyne-set-Em-5)
Patient No.
Before
After
Before
After
Before
After
1 2 3 4 5 6 Mean
207 69 192 206 75 129 146
859 77 506 339 254 226 377
71 33 89 144 37 41 69
473 47 434 222 69 52 216
136 35 93 87 44 82 80
469 25 132 139 172 157 182
P=
.057
.092
‘PAVRo = pulmonary artery input vascular resistance (using PA pressure); PVVRo = pulmonary vein terminal vascular resistance (using PV pressure); PVR o = pulmonary vascular resistance (using AP pressure). P = paired r test, 2 tailed.
vascular resistance rose from 146 to 377 dyne-see-cmm5(P = 0.057), terminal vascular resistance rose from 69 to 216 dyne-seccm+ (P = 0.098), and differential vascular resistance rose from 80 to 182 dyne-set-crnm5
unchanged, going from 15.1% to 14.8% after defect closure. The mean heart rate was unchanged as a result of defect correction; the mean rate was 118 beats/min before correction and 119 beats/min after correction
(P = 0.092).
(P = 0.933).
The significant decrease in the external work of the right heart for all patients as a result of defect closure is shown in Table 4. The total external work decreased from a mean value of 31.8 J/min to 11.4 J/min (P = 0.014). The mean component decreased from 26.7 to 9.8 J/min (P = 0.010) while the oscillatory component decreased from a mean of 5.1 to a mean of 1.6 J/min (P = 0.071). The mean percentage of oscillatory work, however, remained relatively
Pulmonary impedance spectra of the children before and after defect closure are shown in Fig. 1. The solid lines connect the spectra before defect closure: the broken lines connect the spectra after closure. Between 3 and 5 harmonics were measurable for each spectrum. Pressure amplitudes were usually in the noise range at higher frequencies. The significant increase in the input vascular resistance as a result of defect closure for all patients except patient 2 can
TABLE 4 External Work of Right Heart before and after Defect Closure’
Patient No. 1 2 3 4 5 6 Mean P=
Heart rate (beats per min)
TEWR (Joules/min)
MEWR (Joules/min)
OEWR (Joules/min)
Before
After
Before
After
Before
After
Before
118 145 122 83 124 118 118
122 121 111 117 121 121 119
23.6 42.4 25.9 19.0 51.3 28.6 31.8
11.0 10.4 17.2 10.6 10.5 8.8 11.4
19.2 36.7 24.4 15.2 37.6 27.1 26.7
9.1 8.9 16.7 7.8 7.7 8.8 9.8
4.4 5.7 1.5 3.8 13.7 1.6 5.1
.933
.0138
.OlOO
After 2.0 1.6 .5 2.8 2.8 .03 1.6
.0712
%OW Before
After
18.7 13.5 5.9 20.2 26.6 5.6 15.1
17.7 15.0 3.1 26.3 26.3 .3 14.8 .854
‘TEWR = Total external work of right heart; MEWR = mean external work of right heart; OEWR = osczatory external work of right heart; SOW = percent oscillatory external work; P = paired i test, 2 tailed.
LUCAS, WILCOX AND COULTER: ATRIAL
2
4
6
6
IO
12
2
4
6
Frequency
515
SEPTAL DEFECT CLOSURE.
61012
2
4
6
8
IO 12
(Hz 1
FIG. 1. Pulmonary vascular input impedance in children. Data obtained intraoperatively. Solid lines and circles represent spectra before atria1 septal defect closure: broken lines and open circles represent spectra after defect closure.
be seen graphically at 0 Hz. However, the ous minimum.6 As a result of defect closure, modulus values still decreaserapidly, reach- however, there appeared to be a definite ining a minimum value whose magnitude crease in the frequency at which the first would appear to be at least as small as the minimum value was attained in patients 1, 3, minimum value observed in the spectra be- 4, and 5: no obvious shift could be seen in fore defect closure. patients 2 and 6. Owing to the large distance between data DISCUSSION points (approximately 2 Hz) at the heart rates studied, the frequency at which the External Work first modulus minimum might actually be The significant changes in vascular resisattained could only be approximated. Fur- tance and external work as a result of defect thermore, relatively flat configurations such correction can largely be explained by the as those seen for patient 2 before closure and patient 4 after closure could obscure @Forreasons discussed later in the text, the minima the possible local minimum value at a fre- were concluded to be approximately 2 Hz for patient 2 quency lower than the frequency of the obvi- before closure, 6 Hz for patient 4 after closure.
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decrease in pulmonary blood flow in conjunction with relatively stable mean pressure levels: mean blood flow decreased an average of 57%, total external work, TEWR, decreasedan average of 59%. A change in heart rate does not appear to be a major contributing factor [17]: the rate decreased markedly in one patient (patient 2) increasedin another (patient 4), and remained relatively unchanged in the remaining four casesstudied. Although the percentage of oscillatory work, POW, remained relatively unchanged, there was a shift in the distribution of the oscillatory external work, OEWR. Data depicting the relatively larger decrease in the work contribution of the 1st harmonic in comparison to the decrease in TEWR is shown in Table 5. The average decrease in the power in the first harmonic was 74% compared to the average decreasein TEWR of 59% mentioned above, the percentage decreasein the first harmonic being greater than the percentage decreasein TEWR in all but patient 4. The percentage of oscillatory work did not change significantly because the contribution of the first harmonic relative to the higher harmonics decreasedin all patients (Table 5), decreasing from a mean of 78% of OEWR before closure to a mean of 62% after closure. (The negative percentage for patient 6 after closure was not included in the mean). Hence, the higher harTABLE 5 Analysis of Changes in Hydraulic Power Associated with 1st Harmonic before and after Defect Closure % OEWR in 1st harmonic
Patient No.
% Decrease in TEWR
% Decrease in work of 1st harmonic
Before
After
1 2 3 4 5 6
53 15 34 44 80 69
60 78 73 34 88 110
15 83 82 75 71 63
66 64 67 67 45 -33
Mean
59
74
78
62a
‘Negative value for patient 6 not included in calculation of mean.
VOL.
18, NO. 6, JUNE
1975
monies’ contribution as a percentage of OEWR approximately doubled as a result of closure and the raw contribution only decreasedan average of 34% (range 3%-51%). A major contributing factor to this dramatic decrease in the work contribution of the first harmonic is the increase in the absolute value of the phase angle of the first harmonic, 0, (Fig. 1). The increase is marked in patients 1, 3, 5, and 6: slight but negligible in patients 2 and 4. This trend toward an increase in the absolute value of 8, was also sufficient to give the effect of pressure and flow waveforms being more “out of phase” as a result of defect closure. A correlation analysis of the waveforms showed a mean r value of .72 before closure compared to a mean of .48 after closure (P = 0.058). Vascular Impedance: Three-Segment Transmission Line Model
The increase in differential pulmonary vascular resistance by at least 42% in five of the six patients and the changes noted in the impedance spectra, (i.e., the increase in the absolute value of til and the shifts in the frequency of the first modulus minimum) point to an immediate change in the pulmonary vasculature as a result of defect closure. A model similar to, but much simpler than that of Wiener, et al. [23] was used to help interpret the significance of the pattern changes observed. The model assumed that the pulmonary vasculature could be represented by a three-segment transmission line: an arterial segment, a microcirculatory segment, and a venous segment (Fig. 2). Each segment was assumed to be uniform, and to be characterized by three constant (frequency-independent) parameters: resistance (Rr), inertance (L,), and compliance (C,). An etectrical analog of a single segment is shown in Fig. 3.
-1
III-
FIG. 2. Block diagram monary circulation.
of the model of the pul-
LUCAS,WILCOX AND COULTER:ATRIAL SEPTALDEFECTCLOSURE
577
reasonable, an attempt was made to find reliable data on the anatomical and physical characteristics of the human pulmonary circulation for the patients studied. A physiologically and anatomically realistic model FIG. 3. An electricalanalogyof a transmission of the pulmonary vasculature was develline segmentshowingthe distribution of resistance (R), inertance(L), and compliance(0 per unit oped [ 151 as a first step in estimating the values for the model parameters. This basilength(D). cally involved determining a reasonable The numerical values of these parameters branching pattern for the pulmonary vascuwere the same within a given segment but lar tree and defining each relatively uniform were, in general, different in different seg- segment in terms of its length, radius, and ments. In the microcirculatory segment, the wall properties. Measurements based on aniinertance was considered negligible and was mal experiments were used only when hutaken as zero. man data were not available. Finally, Wiener Parameters of this model represent only et al. [24] model specifications for the dog average values in the circulatory segments were used when other data could not be considered. More elaborate models [3, 20, found in the literature or detailed reconstruc22, 241 are available which provide a higher tion of the actual branching pattern seemed degree of approximation to the real system. too complex to be practically applicable for These models, however, involve so many un- the study. A computer program was written determined parameters that their clinical to obtain estimates of total resistance, total applicability is limited at this state of our inertance, and total compliance of each of knowledge and patient-monitoring capabil- the three segments on the basis of the speciity. On the other hand, lumped models or fications of this physiological model and the one-segment transmission line models [5, 231 age, arterial and venous pressures, and anaare too oversimplified or incomplete to be tomical measurements available on each pavery useful. The model used here represents tient. a compromise which provides a rough but Lateral and anterior-posterior angiograms useful guide to interpreting data in terms of of the pulmonary vasculature were availequivalent parameters which indicate the able for three patients. The diameter and state of the pulmonary vasculature. length of the main pulmonary artery were Mathematical details of the model are measured on the lateral views; the diameter given in Appendix I. The computational and length of the right pulmonary artery procedure was as follows. Assuming the and other identifiable vesselswere measured terminal impedance of the venous segment on the anterior-posterior view. All measurewas a pure resistance equal to mean venous ments were multiplied by a correction factor pressure divided by mean pulmonary blood obtained by measuring roentgenograms of ‘a flow, the input impedance of the venous seg- ruler placed in the approximate position of ment could be computed from the equa- the heart. On the basis of the Pollack et al. tions. By hydrodynamic continuity the ter- [20] model, the left pulmonary artery was minal impedance of the microcirculatory estimated to be .95 times as wide and .90 segment was equal to the input impedance times as long as the right pulmonary artery. of the venous segment. This enabled the When angiograms were not available, the input impedance of the microcirculatory seg- diameter of the main pulmonary artery was ment to be computed; and, similarly, the determined from the size of the flow probe input impedance of the arterial segment. used and the length was estimated from In order to obtain initial parameters for angiograms of other patients of comparable the model which would be physiologically age and body surface area. The computer
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program could then estimate the dimensions of all other vessels. Since the actual differential pulmonary vascular resistance was computed for each patient before defect closure, the percentage of that resistance attributable to each segment was estimated; 46% to the arterial segment, 34% to the microcirculatory segment, and 20% to the venous segment. This was based on the findings of Brody et al. [I] in a study of the longitudinal distribution of the pulmonary vascular resistance of dogs. The compliance of the microcirculatory segment (MC) was computed on the basis of Yu’s [27] finding that the capillary blood volume was approximately 54 cc/m2 and Glazier et al.‘s [6] estimate’that the distensibility coefficient of the microcirculatory vessels was 2.5%/ cm H20. The computer program used for the curvefitting procedure was a version of the BMD-X Non-Linear Least Squares program from the BMDX-UCLA Biomedical Series’ modified to be implemented on the IBM 1130.Only four of the parameters, resistance of the microcirculatory segment (MR), arterial resistance (AR), compliance (A,), and inertance (AL) were actually allowed to vary. Preliminary tests of the model had shown that the impedance spectrum was quite insensitive to changes in the parameters of the venous segment when compliances of the arterial and microcirculatory segments were in the ranges thought physiologically realistic for subjects with normal pulmonary pressure. (When compliances are low, e.g., in the hypertensive patient with mitral valve disease,the impedance spectrum becomes quite sensitive to changes in the venous parameters.) Since the inertance of the microcirculatory segment is negligible, the characteristic impedance of that segment is (M,/ jwM,-)i12, hence, an increase in MR and a decreasein M, have similar effects on the impedance spectrum. Therefore, M, was not allowed to vary in the curve-fitting procedure. Demonstration of the direction and ‘ProgramBMDX85Non-LinearLeastSquares.
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18, NO. 6, JUNE
1975
magnitude of possible error as a result of fixing MC is discussedbelow. The independent variable for the procedure was frequency; the dependent variable was either impedance modulus, impedance phase, or hydraulic resistance. Iterations were repeated until reasonable fits were obtained for all three dependent variables. The weighing function for each frequency was directly proportional to the hydraulic power contribution at that frequency, placing emphasis on fitting the impedance values at the lower harmonics. The curve was fit to points from all data sets rather than the average spe&a shown in Fig. 1. Criteria in order of importance were: (1) fit both modulus and phase well for at least first 2 harmonics, (2) coincide first modulus minimum with first indicated zero crossing or inflection of phase angle curve, and (3) coincide modulus maximum following first modulus minimum with 2nd indicated zero crossing or inflection of phase angle curve. Figure 4a (patient 2 preclosure) shows an example of the results when neither zero crossings nor inflections in the phase angle curve were obvious. The model was not capable of fitting phase angle values outside the range -x/2 to ~12 radians. When phase values are outside this range, the hydraulic power is negative, indicating the presence of a source of energy or some other phenomena outside the scope of the passive model. Pressureamplitudes were on the brink of the noise range for harmonics 3 and 4 and within the noise range for harmonic 5. Figure 4b (patient 6 preclosure) shows an example where the three criteria were met, but harmonics 4 and 5 were not considered in the curve-fitting procedure. The flow amplitude of the 4th harmonic ranged from .15 to 7.0 cc/set in the different data sets, yielding impedance values between 6050 and 200 dyne-set-cme5. The results of the curve-fitting procedure to the preclosure impedance spectra are given in Table 6. Only mean values of the five fixed parameters are included. The parameter values for patient 1 were omitted
LUCAS, WILCOX AND COULTER: ATRIAL
579
SEPTAL DEFECT CLOSURE
Certainly the curve-fitting procedure yields a rough approximation at best and the authors recognize the possibility that a model could imitate the impedance spectrum without having a realistic relationship to the components of the system [18]. It was reassuring, however, that the mean estimates of the key parameters were generally consistent with findings in the literature. Original estimates of A, were based on the hypothesis that 46% of PVR was disFIG. 4. Pulmonary vascular input impedance (A) patient 2 and (B) patient 6 before defect closure. Each point represents a different data set. Solid line represents spectrum predicted by parameters of model.
300
3 E
from the means since they appeared to differ significantly from the values of the other five patients. Since the weighing function was proportional to hydraulic power, the fit at 0 Hz was always good; however, there was no guarantee that the sum of the resistances of the three segments plus the terminal resistance would exactly equal the value of the input resistance given in Table 3. A representative preclosure impedance spectrum for the patient population construtted by assuming the parameters of the model were equal to the mean values given in Table 6 is shown in Fig. 5.
200 I
.ij&=--2
4
6
Frequency
8
IO
12
(Hz)
FIG. 5. Average pulmonary vascular input impedance of children before atria1 septal defect closure, Computed for three-segment transmission line model whose parameter values equal the mean values given in Table 6.
TABLE 6 Model Parameters before and after Defect Closure ARK
ALL
(dyne-see-cm-s)
Aca (ems/dyne X 106)
(dyne-set*-cm-s)
MRa (dyne-set-cm-s)
Patient No.
Before
After
Before
After
Before
After
Before
1 2 3 4 5 6
123 29 23 50 11 3
81 I 6 30 3 3
2.23 1.12 2.45 3.32 2.16 1.53
1.11 .94 1.22 2.12 1.96 1.53
700 6000 4270 1120 1390 3240
490 5000 2540 660 830 2540
5 3 50 16 28 59
446 17 82 86 113 118
Mean
23
10
2.24
1.55
3204
2314
31
83
MC (ems/dyne X 106) Before Mean
1385
After
VC
(dyne-se&cm-s)
(ems/dyne
X 106)
Before
After
Before
After
Before
After
14
25
1.70
1.70
2304
3080
1385
A = arterial, M = microcirculatory,
VL
VRa
(dyne-see-cm-s)
After
V = venous, R = resistance, I, = inertance, C = compliance.
aData for patient 1 not included in mean.
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tributed along the arterial segment, Final estimates placed that percentage at 34% before defect correction. Using mean values of QM and A, in the calculation, the pressure drop along the arterial segment would be approximately 3.5 mm Hg. The mean value for A,, 2.24 dyne-se& cme5was smaller than the original estimates made on the basis of angiograms (range 2.77-4.45 dyne-sec2-cme5),but was comparable to findings of other investigators. Shaw (23) calculated a mean value of 1.6 dyne-se&cm-” (range .6-3.4) for the septaldefect patients he studied. Reuben [21] used mean values for (1) frequency of the minimum value of the modulus of the impedance spectrum, (2) arterial compliance, and (3) peripheral vascular resistance to estimate mean arterial inertance. This gave values for pulmonary arterial inertance of 1.72 dyne-sec2-cm-5for patients with normal pulmonary artery pressure and values of 1.97 dyne-sec2-crne5for patients with pulmonary hypertension. Deuchar and Knebel [4] estimated the distensibility of pulmonary arteries of young children by using an equation taken from Windkessel theory. Mean distensibility for children with normal pulmonary vascular dynamics was reported to be .7 ml/mm Hg by age 5, 1.1 ml/mm Hg at age 10, and 1.9 ml/mm Hg at age 20. By comparison, the mean distensibility for two children (age 7 yr) with atrial septal defects was 1.3 ml/mm Hg. Studying a much wider age range (5-40 yr), Shaw [23] used a fourelement model of the pulmonary circulation to estimate the normal distensibility of the pulmonary arterial system to be 3.1 ml/mm Hg and distensibility in septal defect patients to be 8.4 ml/mm Hg. Using the same theory as Engleberg and DuBois, Reuben [21] found an average compliance of 2.87 ml/mm Hg in patients with normal pulmonary pressure; values as low as 0.7 ml/mm Hg were found in patients with severe pulmonary hypertension. If the implications of these findings are correct, i.e., compliance tends to be lower in children
VOL.
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than in adults, but higher in normotensive ASD patients than in patients with normal pulmonary pressures and flows, the mean preclosure estimate of compliance, 4.3 ml/ mm Hg,X obtained by using the threesegment transmission line model seems reasonable. The representative impedance modulus versus frequency curve predicted by this model showed smaller amplitudes fluctuations than those of other models [2, 3, 22, 241. This relatively flat configuration, however, compares favorably with the input impedance spectrum versus frequency data of Milnor et al. [18]. In that study of 10 human subjects (age range 21-38 yr), the pulmonary input impedance modulus fell sharply from relatively high values at 0 frequency to a minimum between 2 and 5 cycles/set and showed only small oscillations at frequencies above this minimum. Since such a model is probably more valuable for determining the direction of change in parameters than in determining accurate estimates of these parameter values, the sensitivity of the model to changes in the arterial and microcirculatory parameters in the neighborhood of the mean values given in Table 6 was examined. The broken lines in Figs. 6 and 7 show graphically the results of these analyses. For each parameter, the decreasescorrespond to 14 M, and x the original values; the increases correspond to fi 2, and 4 times the original values. Changes in A, (Fig. 6a) do not affect the frequency of the modulus minima and maxima, but markedly alter the range of the fluctuation. Decreasing AR results in larger fluctuations in both modulus and phase angle graphs. Increasing A, flattens modulus and phase angle graphs, increasing and making less obvious the first minimum modulus value which would remain at approximately 2 Hz. Small changes in A, have the most dramatic effect on the model (Fig. 6b). De*From Table 6: (3.20 x 10-3cmg/dyne) 103dyne/cm*/mm Hg) = 4.3 ml/mm Hg.
x (I.33 x
LUCAS, WILCOX AND COULTER: ATRIAL
SEF’TAL DEFECT CLOSURE
Frequency
(Hz)
FIG. 6. Sensitivity of input impedance spectrum of three-segment transmission line model to changes in arterial (A) resistance, (B) inertance, and (C) compliance. Solid line represents average spectrum shown in Fig. 5. For parameter decreases, broken lines correspond to I/&, l/2, and l/4 times the original parameter value (Table 6): for parameter increases, broken lines correspond to a 2, and 4 times the original value.
creasing A, raises the frequency but lowers the amplitude of the first modulus minimum; increasing A, has the reverse effect. Decreasing A, markedly raises both the frequency and amplitude of the first modulus maximum; the frequency of the first modulus
minimum is relatively unchanged, though the amplitude increases. Increasing A, (Fig. 6c) lowers both frequency and amplitude of modulus minima and maxima. Figure 7 shows the similarity in the spectrum response to inverse changes in MR and
582
JOURNAL
OF SURGICAL
RESEARCH VOL. 18, NO. 6, JUNE 1975 ---lncrcare
---
Before Atrlal Soptal Dwmarr in
Dhct
in MR
Clown
B. F
200
0 0 G=j 3.14 c c 1.57 a2 0 o u -LB8 8 s -3.14 0’
Frequency
(Hz)
FIG. 7. Sensitivity of input impedance spectrum of three-segment transmission line model to changes in microcirculatory (A) resistance and (B) compliance. Computational procedure same as in Fig. 6.
Mc. Decreasing MR or increasing Mc lowers the frequency at which the first modulus minimum occurs: changes in A4c are more discernible, especially at frequencies lower than 2 Hz. Likewise, increasing MR and decreasing Me have similar effects: the frequency of the first modulus minimum is slightly higher; however, the increase in MR tends to lower the value of that minimum while the decrease in Mc shifts the same value. The sensitivity analysis of the parameters emphasizes the importance of considering phase angle as well as modulus values when determining the frequency of the first minimum modulus value. The flat modulus values and the negative flat phase values
of patient 2 before closure (Figs. I and 4a) make determination of the frequency of the first minimum difficult. A relatively high value of A, was needed to fit such a configuration. However, a small decrease in the value of A, determined by the curve-fitting procedure produces a decrease in the modulus value at approximately 2 Hz, indicating that the first local minimum value occurs at 2 Hz rather than 6 Hz where the first measured minimum is located. The same situation could be the case for patient 4 after defect closure. However, the zero crossing of the phase curve at approximately 5 Hz indicates that the actual first minimum value is probably in the neighborhood of the minimum value measured at 6Hz.
LUCAS,
-3 l4C
WILCOX
AND
COULTER:
ATRIAL
SEPTAL
DEFECT
CLOSURE
583
I$+---2
4
6
a
IO
12
2
4
6
a
IO
12
FIG. 8. Changes in the pulmonary vascular input impedance spectrum in response to atrial septal defect closure predicted by selective changes in parameter values of the three-segment transmission line model. Solid line represents average preclosure spectrum shown in Fig. 5. Broken lines represent postclosure spectra computed as follows. (A) Postclosure differential vascular resistance same percentage distribution between arterial, microcirculatory, and venous segments as preclosure values; (B) total increase in differential pulmonary vascular resistance distributed in microcirculatory segment; (C) model parameter values equal to mean postclosure values given in Table 6.
Postclosure venous parameter values were calculated according to the criteria already given. The terminal impedance was changed to reflect the postclosure ratio of mean venous pressure to mean blood flow. Since there was a measurable increase in differential vascular resistance, the plausible distribution of that increase was first examined. The broken line in Fig. 8a shows the representative impedance spectrum that would be the result of a uniform increase in all segments, i.e., A,, M,, and VR are the same percentage of differential vascular resistance both before and after defect correction. Obviously, this does not agree with the direction of change observed in the actual impedance spectra.
A more satisfactory approach, shown in Fig. 8b, is to assume that all the increase is in the microcirculatory segment. The changes are slight but in the observed direction for most of the patient data: the frequency of the first modulus minimum is higher, the value of that minimum is slightly smaller, and the phase angle around 2 Hz is more negative. However, even a large change in M, would not account for the magnitude of the changes observed in the phase angle graphs of many of the patients. Using initial parameter values computed by the manner illustrated in Fig. 8b, the curve-fitting procedure was repeated for the postclosure impedance data. Except for matching the large positive phase angle value
584
JOURNAL
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RESEARCH
of patient 6 at 2 Hz, the curve-fitting criteria were met and the results are included in Table 6 and illustrated by the broken line in Fig, 8c. Comparison shows that the mean values for A,, A,, and AL decreased. The decrease in A, and A, raised the frequency of the first modulus minimum; the decrease in A, was primarily responsible for lowering the value of that minimum. The procedure was designed to change the value of A, only when realistic changes in other parameters could not obtain the desired results. The decreasemade was often necessary for fitting the more negative phase angle values often observed at 2 Hz. Neither an increase nor a decrease in A, had that effect: increasing A, did not have the desired effect on the modulus curve. Assuming the parameter changes predicted by the curve-fitting procedure are correct, two possible explanations of our findings present themselves for consideration. The first is that the major reflection site, or the juncture of the proposed arterial versus microcirculatory segment, is more proximal as a result of defect closure; hence, total resistance, inertance, and compliance would then be less in the shortened “arterial segment” even if the properties of that proximal segment remained the same.The second explanation is to assume that the three segments of the model continue to correspond to the same divisions of the vasculature, but undergo changesin size and wall properties. In anatomical terms, this possibly corresponds to increased radii of larger arterial vesselssince inertance beyond the 5th or 6th generations of arteries is already negligible, stiffening of the proximal arterial segment, and vasoconstriction or variations in the number and positions of microcirculatory vessels that are perfused. Interestingly, this response is almost identical to the response of the impedance spectrum to serotonin infusion modeled by Pollack et al. 1201. SUMMARY Results related to mean pressure and flow measurements were in the anticipated direc-
VOL.
18, NO. 6, JUNE
1975
tion. Pulmonary blood flow described as a result of defect closure and pulmonary pressures, in the normal range before closure, tended to remain the same; hence, the external work of the right heart decreased significantly. Changes in the differential pulmonary vascular resistance and the impedance spectrum indicated that there was an immediate pulmonary vascular response to defect closure. After closure, the differential pulmonary vascular resistance tended to increase, the frequency of the first minimum value of the impedance modulus curve tended to be higher, and the absolute value of the phase angle of the first harmonic tended to be larger. Analysis using a threesegment transmission line model suggests that closure of atria1 septal defects results in changes in the pulmonary circulation characterized by either (1) changes in the major reflection’ site or (2) dilatation and stiffening of proximal arterial vessels accompanied by vasoconstriction or decreased number of microcirculatory vesselsperfused. The parameters of the model are also being computed for a group of adult patients with atria1 septal defects and a group of normotensive children with ventricular septal defects. Comparisons of the parameter values and/or changes in the parameter values as a result of defect correction in these patients may offer additional insight into causes of the changes observed in the impedance spectra as a result of defect closure. APPENDIX I Equations Describing the Transmission Line Model Each segment of the transmission line model is assumed to be uniform and to be characterized by four constant (frequency independent) parameters: R = resistance per unit length; L = inertance per unit length; C = compliance per unit length; D = length of segment. Associated with each segment are four characteristic quantities obtained from standard transmission line theory [7]:
LUCAS. WILCOX AND COULTER: ATRIAL
1. The characteristic impedance Z,,, z, = ((R +jwL)/jwC)“2,
Q
585
SEPTAL DEFECT CLOSURE
=
Qp
‘p e-~* + “,
(1)
1
‘p Eve. 0
(9)
where w = angular frequency, j = fl
If the input impedance of each segment is the only quantity of interest, it can be y = CjwC(R + jwL))‘j2 shown that D can be eliminated as an inde(2) pendent variable and the equations simpli= M,e@ 7 = a + j@, fied by defining where M, = modulus;’ Br = phase angle; R, = RD. (10) (Y = attenuation per unit length; /3 = phase shift per unit length. L, = LD. (11) 3. The reflection coefficient, given by C, = CD. (12) 2. The complex wave number y, given by
r = -z, - ei is, + z,’
(3)
Then
where Z,, = terminal impedance of segment, which is equal to the input impedance of where the ensuing segment. 4. The input impedance of asegment Z,, given by z = z 1 - Ie-2rD 0 P 1 + Iee2TD = 1Z, 1,ej@= 24+ jv,
(4)
where u = hydraulic resistance; v = hydraulic reactance. The instantaneous values of pressure and flow, p and q, may be expressed in terms of their complex amplitudes, P and Q: p = Real(Pej”‘]. q = ReallQej”‘).
=
PP -.
Qp
O)
(6)
(7)
At any distance x from the proximal end of the segment, the complex amplitudes for the pressure and flow are P = Pp
zp+ zoemv*+ 22,
(13)
Z. =((RT + joLT)/jwCT)1/2
(14)
-yT = yD = (juC,(R,
+ jwLT))1/2.(15)
Calculation begins by assuming the terminal impedance of the venous segment to be a pure resistance equal to mean venous pressure divided by mean pulmonary blood flow. ACKNOWLEDGMENTS The authors express their appreciation to Nancy Wooten, Frank Boone, and Carol Porter for their assistancein this work.
REFERENCES
Hence, if the pressure (P,) and flow (Q,) at the proximal end of the segment are known, the input impedance can also be computed as zp
z = z 1 - IeSZYT 0 P 1 + Fe-2yT’
1
zp - zo evx 22, ’
(8)
1. Brody, J. S., Stemmler, E. J., and Dubois, A. B. Longitudinal distribution of vascular resistance in the pulmonary arteries, capillaries, and veins. J. Clin. Invest. 47783-199, 1968. 2. Caro, C. G., and McDonald, D. A. The relation of pulsatile pressure and flow- in the pulmonary vascular bed. J. Physiol. 157:426453, 1961. 3. dePater, L. An electrical analogue of the human circulatory system. Ph.D. Dissertation, University of Groningen, Netherlands, 1966. 4. Deuchar, D. C., and Knebel, R. The pulmonary and systemic circulations in congenital heart disease. bit.
Heart J. 14:225-249, 1952.
5 Engelberg, J., and Dubois, A. B. Mechanics of pulmonary circulation in isolated rabbit lungs. Amer. J. Physiol. 1%:401-414, 1959.
6. Glazier, J. B., Hughes, J. M. B., Maloney, J. E., and West, J. B. Measurements of capillary dimensions and blood volume in rapidly frozen lungs. J. Appl. Physiol. 26:65-16, 1969.
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RESEARCH VOL. 18, NO. 6, JUNE 1975
7. Goldman, S. Luplace Transform Theory and Electrical Transients. Dover Pub., New York: 1966. 8. Heath, D., and Edwards, J. E., The pathology of hypertensive pulmonary vascular disease:A description of six grades of structural changes in the pulmonary arteries with special reference to congenital cardiac septal defects. Circulation l&533537, 1958. 9. Heath, D., Helmholz, H. F., Jr., Burchell, H. B., Dushane, J. W., and Edwards, J. E. Graded pulmonary vascular changes and hemodynamic findings in cases of atrial and ventricular septal defect and patent ductus arteriosus. Circulation
19:467-480, 1966. IS. Milnor, W. R., Conti, C. R., Lewis, K.
B., O’Rourke, M. F. Pulmonary arterial pulse wave velocity and impedance in man. Circ. Res. 25:627649, 1969.
18:1155-1166, 1958.
10. Heath, D., Helmholz, H. F., Jr., Burchell, H. B., Dushane, J. W., and Edwards, J. E. Relation be tween structural changes in the small pulmonary arteries and the immediate reversibility of pulmonary hypertension following closure of ventricular and atria1 septal defects. Circulation 18:1167-l 174, 1958.
11. Heath, D., Wood, E. H., Dushane, J. W., and Edwards, J. E. The structure of the pulmonary trunk at different ages and in cases of pulmonary hypertension and pulmonary stenosis. J. Parhol. Bacterial 77:443-456,
Dissertation, University of North Carolina, Chapel Hill, North Carolina, 1973. 16. McGoon, D. C., Swan, J. H. C., Brandenburg, R. O., Connolly, D. C., and Kirklin, J. W. Atria1 Septal Defect: Factors Affecting the Surgical Mortality Rate. Circulation 19:195-200, 1959. 17. Milnor, W. R., Bergel, D. H., and Bargainer, J. D. Hydraulic power associated with pulmonary blood flow and its relation to heart rate. Circ. Res.
1959.
12. Heath, D., Wood, E. H., Dushane, J. W., and Edwards, J. E. The relation of age and blood pressure to atheroma of the pulmonary arteries and thoracic aorta in congenital heart disease. Lab. Invest. 9~259-272, 1960.
13. Honda, T., Horiuchi, T. A., Koyamada, K., Ishitoya, T., and Ishizawa, E. Histometrical study of the pulmonary arteries in normal postnatal development and in patients with ventricular septal defect. Tohoku J. Exp. Med. 102:403-412, 1970. 14. Jarmakani, J. M. M., Graham, T. P., Jr., Benson, D. W., Jr., Canent, R. V., Jr., and Greenfield, J. W., Jr. In vivo pressure-radius relationships of the pulmonary artery of children with congenital heart disease. Circulation 43:585-592, 1971. 15. Lucas, C. Pulmonary input impedance spectrum of children with atria1 and ventricular septal defects: A computer simulation study based on a three segment transmission line model. Ph.D.
19. Patel, D. J., Defreitas, F. M., and Fry, D. L. Hydraulic input impedance to aorta and pulmonary artery in dogs. J. Appl. Physiol. 18:134-139, 1963. 20. Pollack, G. H., Reddy, R. V., and Noordergraaf,
A. Input impedance, wave travel, and reflections in the human pulmonary arterial tree: Studies using an electrical analog. IEEE Trans. Bio-Med. Eng. BME 15:151-164, 1968. 21. Reuben, S..R. Compliance of the human pulmonary arteriat system in disease. Circu. Res. 29:4050,1971. 22. Rideout, V. C., and Katra, J. A. Computer simu-
lation of the pulmonary cardiovascular system. Sitnularion 12:239-245, 1969.
23. Shaw, D. B. Compliance and inertance in the pulmonary arterial system. Clin. Sci. 25:181-193, 1963. 24. Wiener, F., Morkin, E., Skalak, R., and Fishman,
A. P. Wave propagation in the pulmonary circulation. Circ. Res. 19:834-850, 1966. 25. Wilcox, B. R., Croom, R. D. III, and Coulter, N. A., Jr. Changes in pulmonary vascular dynamics following closure of atrial septal defects in man. Ann. Thorac. Surg. 9:41 l-418, 1970. 26. Wilcox, B. R., Lucas, C., and Coulter, N. A., Jr. Effect of septal defect closure on the external work of the heart in children. Ann. Surg. 176:485490, 1972. 27. Yu, P. N. Pulmonary Blood Volume in Health and Disease. Lee & Febiger, Philadelphia, PA, 1967.
OF SURGICAL
RESEARCH
18,
571-586 (1975)
Pulmonary Atrial
Septal
Vascular Defect
Response
Closure
to
in Children
1
CAROL L. LUCAS, PH.D., BENSON R. WILCOX, M.D., AND NORMAN A. COULTER, JR., M.D. Division of Cardiothoracic Surgery, University of North Carolina School of Medicine, Chapel Hill, North Carolina 27514 Submitted for publication July 20, 1974
Pulmonary vascular disease increases the risk in performing corrective surgery in patients with heart disease; therefore, reliable techniques for determining the extent of the pulmonary vascular impairment have been sought [g-10, 161.Identification of the hemodynamic factors responsible for the pathogenesisof the diseaseshould also aid in evaluating the status of the patient’s pulmonary vasculature; hence, studies have been done which sought to demonstrate correlation between abnormal pulmonary vasculature development with abnormal hemodynamic variables [ 1l-141. Studies previously done in this laboratory indicate that pulsatile pressure and flow parameters may prove more helpful than the mean pressure and flow values in studying pulmonary hemodynamics [15, 25, 26). The purpose of this investigation was to examine pulmonary vascular dynamics in good surgical risk children before and after atria1 septal defect closure in order to: (1) establish normative values for several impedance-related parameters for this patient population, and (2) understand better the immediate response of the pulmonary vasculature to corrective surgery. A three-segment transmission line model of the pulmonary circulation was used to interpret changes observed in the pulmonary input impedance spectrum as a result of defect correction. ‘Supported by USPHS Grant HL-I 1919-06and NIH Fellowship 4 FOl GM46707-03 STAT.
METHODS Patient Material and Data Acquisition
Pressure and flow data were obtained from six children at the time of atria1 septal defect closure. No patients with endocardial cushion defects or other congenital heart diseases were included. Table 1 lists the patient’s diagnosis, age, sex, and body surface area at the time of operation, as well as the pulmonary arterial pressures and pulmonary-to-systemic blood flow ratios measured at preoperative cardiac catheterization. With the patient under general anesthesia (halothane or fluroxene and oxygen), the heart was exposed through a median sternotomy. The main pulmonary artery was isolated and a flow probe2 of appropriate size was positioned to measure pulsatile blood flow. The amplitude response of the flow probe was flat at 10 Hz and showed less than 2.5% error at 15 Hz; the phase response showed a flat 7 msec time lag, or a linear phase shift of 2.52”/Hz, up to 20 Hz. Pressures were measured through 2-in. 20gauge needles attached by 72-in. large-bore (i.d. 3 mm) saline-filled catheters to a Statham differential manometer (Model ~23H).~ Connections were made so that the right superior pulmonary venous pressure was *Carolina Medical Electronic SquareWave Electromagnetic Flowmeter, Model 321, Series 500 flow probes. King, NC. sStatham Medical Instruments, Inc., Los Angeles, CA.
571 Copyright @1975by Academic Press, Inc. All rights of reproduction in any form reserved.
572
JOURNAL OF SURGICAL RESEARCH VOL. 18, NO. 6, JUNE 1975 TABLE 1 PreoperativeData
ilarly shaped pulses were selected for further processing. Only pulses not obviously showPatient Age,’ PA,b ing the effects of respiration, e.g., the raised No. sex BSA’ Qp/Qsb PA(S/D)b (mm Hg) baseline of the pulmonary artery pressure pulse, were chosen. A pattern recognition 1 4F .69 3.60 48116 26 .84 24104 15 2 SM 1.70 procedure was used to filter the signal and 3 6F .80 2.40 23105 12 remove spikelike artifacts. An autocorrela4 25/08 1.5 6M .79 1.90 tion procedure then determined the exact 5 3M .85 1.60 32108 16 beginning and ending points of each of the n 23109 14 9M .92 1.30 6 pulses and the selected curves over the re‘Age and body surfacearea(BSA) at operation. bFlow ratio (Qp/Qs) and pulmonary artery systolic, fined period of observation, 7, were disdiastolic, and meanpressureat cardiaccatheterization. played on the scope to determine the success of spike removal and selection procedures. recorded directly as well as being automatically subtracted from the pressure measured Fourier Analysis in the main pulmonary artery distal to the Fourier analyses of 10n harmonics were flow probe. The amplitude response of the then performed upon pressure and flow pressure-sensingsystem was flat at 5 Hz and waveforms, giving showed a 40% increase in sensitivity at 10 IOII Hz; the natural frequency was approximately P = PO + c P,sin(kwt + &) (1) 20 Hz. Flow and pressure signals were rek-l corded on magnetic tape for later computer IOII analysis. These measurements were made (2) prior to defect closure and before cannulak-l tion was performed. Postclosure values were where P = pressure; PO = mean pressure; recorded only after cannulae were removed Pk = amplitude of Kth pressure harmonic; and patient was judged to be stable hemodk = phase of Kth pressure harmonic; w = dynamically. Thus, each patient served as 27r/7; Q = flow; Q, = mean flow; Qk = amhis own control in that all data analysis plitude of Kth flow harmonic; qk = phase of was carried out in terms of change in preKth flow harmonic. closure versus postclosure measurements. The information obtained from the analyData Selection seswas used for computing all other paramThe initial step in handling of data was eters, and no other smoothing technique was the selection of analog data collected during employed. The Fourier coefficients and operation; specifically, (1) pulsatile pul- phase angles, the impedance and power monary blood flow, (2) pulmonary input spectrum values, and other key parameters pressure, (3) pulmonary differential pressure, (e.g., pressures and flow, resistance values, and (4) pulmonary venous pressure. A gen- cardiac output, etc.) were then printed as
Q= Qo+c Qksi@t+ *,),
eral purpose
program
sampled all
taped
channels simultaneously. Utilizing a Raytheon analog to digital converter equipped with a Tektronix 611 oscilloscope,5 the data were analyzed and stored in integer form on the disk of an IBM 1130digital computer. Sections of data consisting of n(2-4) sim‘ComputerHardware,Inc., Sacramento,CA. JTektronix,Inc., Seattle,WA.
well as stored on statistical
retrieval
and
master patient file disks. External Work The average power of the pressure and flow waves generated by the right heart (w) was computed as the sum of a mean (M) and an oscillatory (0) component, i.e.,
W=M+O,
LUCAS, WILCOX AND COULTER: ATRIAL
573
SEPTAL DEFECT CLOSURE
aging selected points from all the data sets for each harmonic. A point was included in IOIl the average if the flow modulus was greater 0 = + c PkQkcos(qbp - ‘I’,). (3) than 3 ml/set and the pressure modulus k-l The total external work of the right heart was greater than .4 mm Hg. Standard deviaper minute (TEWR) could then also be tions at each frequency were small when divided into mean (MEWR) and oscillatory these criteria were met. (OEWR) components: RESULTS Values for pulmonary blood flow and TEWR = MEWR + OEWR, mean arterial, venous, and differential preswhere MEWR = 60 M, OEWR = 60 0. (4) sures measured in the operating room are It should be noted that this is an approxi- given in Table 2. Pulmonary blood flow demate measure of external work since it does creased by at least 44% for each patient, not include kinetic energy, considered negli- with the average flow decreasing from 11.54 liters per minute to 4.68 liters per minute gible under these conditions. (P = 0.008) after closure. Mean pulmonary Impedance Spectrum artery and pulmonary vein pressures reThe pulmonary vascular input impedance mained relatively unchanged. The average of spectrum was calculated for each section of the pulmonary artery mean pressures dedata processed. The impedance of the Kth creased from 17.9 mm Hg to 17.7 mm Hg harmonic was (P = 0.951) after closure while mean pulmonary vein pressure rose from 8.3 mm Hg Z(h) = ) Z, ) ejek, (5) to 10.2 mm Hg (P = 0.563) after closure. where 1Zk ) = P,/Q, = modulus and f& = However, both pressures decreased in four & - \k, = phase. patients and markedly increased in two patients (patients 1 and 3). Differential pressure Only harmonics which were multiples of the decreasedor remained relatively unchanged heart rate were considered since intermediate for all patients, the average value decreasing harmonics usually had pressure or flow am- from 9.9 to 8.3 mm Hg (P = 0.185). plitudes within the noise range of the instruValues for input, terminal, and differenmentation. Representative impedance spec- tial resistances are given in Table 3. All tra for each patient both before and after resistance values rose with the exception of defect correction were constructed by aver- differential resistance in patient 2. Input where M = P,,Q,,
TABLE 2 Mean Pressure and Flow before and after Defect Closure
Qm
Patient
(liters/min)
P*m
(mmHg)
pvm
(mmHg)
APItl
(mmHg)
No.
Before
After
Before
After
Before
After
Before
After
1 2 3 4 5 6 Mean
7.45 17.83 8.74 6.64 17.37 11.22 11.54
2.51 8.31 4.44 3.71 4.27 4.83 4.68
19.3 15.4 20.9 17.1 16.2 19.1 17.9
27.0 8.0 28.1 15.7 13.6 13.7 17.7
6.8 7.4 9.7 12.0 8.0 5.7 8.3
14.9 4.9 24.2 10.3 3.7 3.2 10.2
12.7 7.8 10.2 7.3 9.5 11.6 9.9
14.8 2.6 7.3 6.4 9.2 9.5 8.3
P=
.008
,951
.563
.185
Q, = pulmonary blood flow; PA, = pulmonary artery mean pressure;PVm = pulmonary vein mean pressure; AP, = differential pulmonary vascular pressure; P = paired t test, 2 tailed.
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TABLE 3 Vascular Resistance before and after Defect Closure’ PAVRu (dyne-set-cm-s)
PWRo (dyne-see-c&)
PVRn (dyne-set-Em-5)
Patient No.
Before
After
Before
After
Before
After
1 2 3 4 5 6 Mean
207 69 192 206 75 129 146
859 77 506 339 254 226 377
71 33 89 144 37 41 69
473 47 434 222 69 52 216
136 35 93 87 44 82 80
469 25 132 139 172 157 182
P=
.057
.092
‘PAVRo = pulmonary artery input vascular resistance (using PA pressure); PVVRo = pulmonary vein terminal vascular resistance (using PV pressure); PVR o = pulmonary vascular resistance (using AP pressure). P = paired r test, 2 tailed.
vascular resistance rose from 146 to 377 dyne-see-cmm5(P = 0.057), terminal vascular resistance rose from 69 to 216 dyne-seccm+ (P = 0.098), and differential vascular resistance rose from 80 to 182 dyne-set-crnm5
unchanged, going from 15.1% to 14.8% after defect closure. The mean heart rate was unchanged as a result of defect correction; the mean rate was 118 beats/min before correction and 119 beats/min after correction
(P = 0.092).
(P = 0.933).
The significant decrease in the external work of the right heart for all patients as a result of defect closure is shown in Table 4. The total external work decreased from a mean value of 31.8 J/min to 11.4 J/min (P = 0.014). The mean component decreased from 26.7 to 9.8 J/min (P = 0.010) while the oscillatory component decreased from a mean of 5.1 to a mean of 1.6 J/min (P = 0.071). The mean percentage of oscillatory work, however, remained relatively
Pulmonary impedance spectra of the children before and after defect closure are shown in Fig. 1. The solid lines connect the spectra before defect closure: the broken lines connect the spectra after closure. Between 3 and 5 harmonics were measurable for each spectrum. Pressure amplitudes were usually in the noise range at higher frequencies. The significant increase in the input vascular resistance as a result of defect closure for all patients except patient 2 can
TABLE 4 External Work of Right Heart before and after Defect Closure’
Patient No. 1 2 3 4 5 6 Mean P=
Heart rate (beats per min)
TEWR (Joules/min)
MEWR (Joules/min)
OEWR (Joules/min)
Before
After
Before
After
Before
After
Before
118 145 122 83 124 118 118
122 121 111 117 121 121 119
23.6 42.4 25.9 19.0 51.3 28.6 31.8
11.0 10.4 17.2 10.6 10.5 8.8 11.4
19.2 36.7 24.4 15.2 37.6 27.1 26.7
9.1 8.9 16.7 7.8 7.7 8.8 9.8
4.4 5.7 1.5 3.8 13.7 1.6 5.1
.933
.0138
.OlOO
After 2.0 1.6 .5 2.8 2.8 .03 1.6
.0712
%OW Before
After
18.7 13.5 5.9 20.2 26.6 5.6 15.1
17.7 15.0 3.1 26.3 26.3 .3 14.8 .854
‘TEWR = Total external work of right heart; MEWR = mean external work of right heart; OEWR = osczatory external work of right heart; SOW = percent oscillatory external work; P = paired i test, 2 tailed.
LUCAS, WILCOX AND COULTER: ATRIAL
2
4
6
6
IO
12
2
4
6
Frequency
515
SEPTAL DEFECT CLOSURE.
61012
2
4
6
8
IO 12
(Hz 1
FIG. 1. Pulmonary vascular input impedance in children. Data obtained intraoperatively. Solid lines and circles represent spectra before atria1 septal defect closure: broken lines and open circles represent spectra after defect closure.
be seen graphically at 0 Hz. However, the ous minimum.6 As a result of defect closure, modulus values still decreaserapidly, reach- however, there appeared to be a definite ining a minimum value whose magnitude crease in the frequency at which the first would appear to be at least as small as the minimum value was attained in patients 1, 3, minimum value observed in the spectra be- 4, and 5: no obvious shift could be seen in fore defect closure. patients 2 and 6. Owing to the large distance between data DISCUSSION points (approximately 2 Hz) at the heart rates studied, the frequency at which the External Work first modulus minimum might actually be The significant changes in vascular resisattained could only be approximated. Fur- tance and external work as a result of defect thermore, relatively flat configurations such correction can largely be explained by the as those seen for patient 2 before closure and patient 4 after closure could obscure @Forreasons discussed later in the text, the minima the possible local minimum value at a fre- were concluded to be approximately 2 Hz for patient 2 quency lower than the frequency of the obvi- before closure, 6 Hz for patient 4 after closure.
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decrease in pulmonary blood flow in conjunction with relatively stable mean pressure levels: mean blood flow decreased an average of 57%, total external work, TEWR, decreasedan average of 59%. A change in heart rate does not appear to be a major contributing factor [17]: the rate decreased markedly in one patient (patient 2) increasedin another (patient 4), and remained relatively unchanged in the remaining four casesstudied. Although the percentage of oscillatory work, POW, remained relatively unchanged, there was a shift in the distribution of the oscillatory external work, OEWR. Data depicting the relatively larger decrease in the work contribution of the 1st harmonic in comparison to the decrease in TEWR is shown in Table 5. The average decrease in the power in the first harmonic was 74% compared to the average decreasein TEWR of 59% mentioned above, the percentage decreasein the first harmonic being greater than the percentage decreasein TEWR in all but patient 4. The percentage of oscillatory work did not change significantly because the contribution of the first harmonic relative to the higher harmonics decreasedin all patients (Table 5), decreasing from a mean of 78% of OEWR before closure to a mean of 62% after closure. (The negative percentage for patient 6 after closure was not included in the mean). Hence, the higher harTABLE 5 Analysis of Changes in Hydraulic Power Associated with 1st Harmonic before and after Defect Closure % OEWR in 1st harmonic
Patient No.
% Decrease in TEWR
% Decrease in work of 1st harmonic
Before
After
1 2 3 4 5 6
53 15 34 44 80 69
60 78 73 34 88 110
15 83 82 75 71 63
66 64 67 67 45 -33
Mean
59
74
78
62a
‘Negative value for patient 6 not included in calculation of mean.
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monies’ contribution as a percentage of OEWR approximately doubled as a result of closure and the raw contribution only decreasedan average of 34% (range 3%-51%). A major contributing factor to this dramatic decrease in the work contribution of the first harmonic is the increase in the absolute value of the phase angle of the first harmonic, 0, (Fig. 1). The increase is marked in patients 1, 3, 5, and 6: slight but negligible in patients 2 and 4. This trend toward an increase in the absolute value of 8, was also sufficient to give the effect of pressure and flow waveforms being more “out of phase” as a result of defect closure. A correlation analysis of the waveforms showed a mean r value of .72 before closure compared to a mean of .48 after closure (P = 0.058). Vascular Impedance: Three-Segment Transmission Line Model
The increase in differential pulmonary vascular resistance by at least 42% in five of the six patients and the changes noted in the impedance spectra, (i.e., the increase in the absolute value of til and the shifts in the frequency of the first modulus minimum) point to an immediate change in the pulmonary vasculature as a result of defect closure. A model similar to, but much simpler than that of Wiener, et al. [23] was used to help interpret the significance of the pattern changes observed. The model assumed that the pulmonary vasculature could be represented by a three-segment transmission line: an arterial segment, a microcirculatory segment, and a venous segment (Fig. 2). Each segment was assumed to be uniform, and to be characterized by three constant (frequency-independent) parameters: resistance (Rr), inertance (L,), and compliance (C,). An etectrical analog of a single segment is shown in Fig. 3.
-1
III-
FIG. 2. Block diagram monary circulation.
of the model of the pul-
LUCAS,WILCOX AND COULTER:ATRIAL SEPTALDEFECTCLOSURE
577
reasonable, an attempt was made to find reliable data on the anatomical and physical characteristics of the human pulmonary circulation for the patients studied. A physiologically and anatomically realistic model FIG. 3. An electricalanalogyof a transmission of the pulmonary vasculature was develline segmentshowingthe distribution of resistance (R), inertance(L), and compliance(0 per unit oped [ 151 as a first step in estimating the values for the model parameters. This basilength(D). cally involved determining a reasonable The numerical values of these parameters branching pattern for the pulmonary vascuwere the same within a given segment but lar tree and defining each relatively uniform were, in general, different in different seg- segment in terms of its length, radius, and ments. In the microcirculatory segment, the wall properties. Measurements based on aniinertance was considered negligible and was mal experiments were used only when hutaken as zero. man data were not available. Finally, Wiener Parameters of this model represent only et al. [24] model specifications for the dog average values in the circulatory segments were used when other data could not be considered. More elaborate models [3, 20, found in the literature or detailed reconstruc22, 241 are available which provide a higher tion of the actual branching pattern seemed degree of approximation to the real system. too complex to be practically applicable for These models, however, involve so many un- the study. A computer program was written determined parameters that their clinical to obtain estimates of total resistance, total applicability is limited at this state of our inertance, and total compliance of each of knowledge and patient-monitoring capabil- the three segments on the basis of the speciity. On the other hand, lumped models or fications of this physiological model and the one-segment transmission line models [5, 231 age, arterial and venous pressures, and anaare too oversimplified or incomplete to be tomical measurements available on each pavery useful. The model used here represents tient. a compromise which provides a rough but Lateral and anterior-posterior angiograms useful guide to interpreting data in terms of of the pulmonary vasculature were availequivalent parameters which indicate the able for three patients. The diameter and state of the pulmonary vasculature. length of the main pulmonary artery were Mathematical details of the model are measured on the lateral views; the diameter given in Appendix I. The computational and length of the right pulmonary artery procedure was as follows. Assuming the and other identifiable vesselswere measured terminal impedance of the venous segment on the anterior-posterior view. All measurewas a pure resistance equal to mean venous ments were multiplied by a correction factor pressure divided by mean pulmonary blood obtained by measuring roentgenograms of ‘a flow, the input impedance of the venous seg- ruler placed in the approximate position of ment could be computed from the equa- the heart. On the basis of the Pollack et al. tions. By hydrodynamic continuity the ter- [20] model, the left pulmonary artery was minal impedance of the microcirculatory estimated to be .95 times as wide and .90 segment was equal to the input impedance times as long as the right pulmonary artery. of the venous segment. This enabled the When angiograms were not available, the input impedance of the microcirculatory seg- diameter of the main pulmonary artery was ment to be computed; and, similarly, the determined from the size of the flow probe input impedance of the arterial segment. used and the length was estimated from In order to obtain initial parameters for angiograms of other patients of comparable the model which would be physiologically age and body surface area. The computer
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program could then estimate the dimensions of all other vessels. Since the actual differential pulmonary vascular resistance was computed for each patient before defect closure, the percentage of that resistance attributable to each segment was estimated; 46% to the arterial segment, 34% to the microcirculatory segment, and 20% to the venous segment. This was based on the findings of Brody et al. [I] in a study of the longitudinal distribution of the pulmonary vascular resistance of dogs. The compliance of the microcirculatory segment (MC) was computed on the basis of Yu’s [27] finding that the capillary blood volume was approximately 54 cc/m2 and Glazier et al.‘s [6] estimate’that the distensibility coefficient of the microcirculatory vessels was 2.5%/ cm H20. The computer program used for the curvefitting procedure was a version of the BMD-X Non-Linear Least Squares program from the BMDX-UCLA Biomedical Series’ modified to be implemented on the IBM 1130.Only four of the parameters, resistance of the microcirculatory segment (MR), arterial resistance (AR), compliance (A,), and inertance (AL) were actually allowed to vary. Preliminary tests of the model had shown that the impedance spectrum was quite insensitive to changes in the parameters of the venous segment when compliances of the arterial and microcirculatory segments were in the ranges thought physiologically realistic for subjects with normal pulmonary pressure. (When compliances are low, e.g., in the hypertensive patient with mitral valve disease,the impedance spectrum becomes quite sensitive to changes in the venous parameters.) Since the inertance of the microcirculatory segment is negligible, the characteristic impedance of that segment is (M,/ jwM,-)i12, hence, an increase in MR and a decreasein M, have similar effects on the impedance spectrum. Therefore, M, was not allowed to vary in the curve-fitting procedure. Demonstration of the direction and ‘ProgramBMDX85Non-LinearLeastSquares.
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magnitude of possible error as a result of fixing MC is discussedbelow. The independent variable for the procedure was frequency; the dependent variable was either impedance modulus, impedance phase, or hydraulic resistance. Iterations were repeated until reasonable fits were obtained for all three dependent variables. The weighing function for each frequency was directly proportional to the hydraulic power contribution at that frequency, placing emphasis on fitting the impedance values at the lower harmonics. The curve was fit to points from all data sets rather than the average spe&a shown in Fig. 1. Criteria in order of importance were: (1) fit both modulus and phase well for at least first 2 harmonics, (2) coincide first modulus minimum with first indicated zero crossing or inflection of phase angle curve, and (3) coincide modulus maximum following first modulus minimum with 2nd indicated zero crossing or inflection of phase angle curve. Figure 4a (patient 2 preclosure) shows an example of the results when neither zero crossings nor inflections in the phase angle curve were obvious. The model was not capable of fitting phase angle values outside the range -x/2 to ~12 radians. When phase values are outside this range, the hydraulic power is negative, indicating the presence of a source of energy or some other phenomena outside the scope of the passive model. Pressureamplitudes were on the brink of the noise range for harmonics 3 and 4 and within the noise range for harmonic 5. Figure 4b (patient 6 preclosure) shows an example where the three criteria were met, but harmonics 4 and 5 were not considered in the curve-fitting procedure. The flow amplitude of the 4th harmonic ranged from .15 to 7.0 cc/set in the different data sets, yielding impedance values between 6050 and 200 dyne-set-cme5. The results of the curve-fitting procedure to the preclosure impedance spectra are given in Table 6. Only mean values of the five fixed parameters are included. The parameter values for patient 1 were omitted
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Certainly the curve-fitting procedure yields a rough approximation at best and the authors recognize the possibility that a model could imitate the impedance spectrum without having a realistic relationship to the components of the system [18]. It was reassuring, however, that the mean estimates of the key parameters were generally consistent with findings in the literature. Original estimates of A, were based on the hypothesis that 46% of PVR was disFIG. 4. Pulmonary vascular input impedance (A) patient 2 and (B) patient 6 before defect closure. Each point represents a different data set. Solid line represents spectrum predicted by parameters of model.
300
3 E
from the means since they appeared to differ significantly from the values of the other five patients. Since the weighing function was proportional to hydraulic power, the fit at 0 Hz was always good; however, there was no guarantee that the sum of the resistances of the three segments plus the terminal resistance would exactly equal the value of the input resistance given in Table 3. A representative preclosure impedance spectrum for the patient population construtted by assuming the parameters of the model were equal to the mean values given in Table 6 is shown in Fig. 5.
200 I
.ij&=--2
4
6
Frequency
8
IO
12
(Hz)
FIG. 5. Average pulmonary vascular input impedance of children before atria1 septal defect closure, Computed for three-segment transmission line model whose parameter values equal the mean values given in Table 6.
TABLE 6 Model Parameters before and after Defect Closure ARK
ALL
(dyne-see-cm-s)
Aca (ems/dyne X 106)
(dyne-set*-cm-s)
MRa (dyne-set-cm-s)
Patient No.
Before
After
Before
After
Before
After
Before
1 2 3 4 5 6
123 29 23 50 11 3
81 I 6 30 3 3
2.23 1.12 2.45 3.32 2.16 1.53
1.11 .94 1.22 2.12 1.96 1.53
700 6000 4270 1120 1390 3240
490 5000 2540 660 830 2540
5 3 50 16 28 59
446 17 82 86 113 118
Mean
23
10
2.24
1.55
3204
2314
31
83
MC (ems/dyne X 106) Before Mean
1385
After
VC
(dyne-se&cm-s)
(ems/dyne
X 106)
Before
After
Before
After
Before
After
14
25
1.70
1.70
2304
3080
1385
A = arterial, M = microcirculatory,
VL
VRa
(dyne-see-cm-s)
After
V = venous, R = resistance, I, = inertance, C = compliance.
aData for patient 1 not included in mean.
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tributed along the arterial segment, Final estimates placed that percentage at 34% before defect correction. Using mean values of QM and A, in the calculation, the pressure drop along the arterial segment would be approximately 3.5 mm Hg. The mean value for A,, 2.24 dyne-se& cme5was smaller than the original estimates made on the basis of angiograms (range 2.77-4.45 dyne-sec2-cme5),but was comparable to findings of other investigators. Shaw (23) calculated a mean value of 1.6 dyne-se&cm-” (range .6-3.4) for the septaldefect patients he studied. Reuben [21] used mean values for (1) frequency of the minimum value of the modulus of the impedance spectrum, (2) arterial compliance, and (3) peripheral vascular resistance to estimate mean arterial inertance. This gave values for pulmonary arterial inertance of 1.72 dyne-sec2-cm-5for patients with normal pulmonary artery pressure and values of 1.97 dyne-sec2-crne5for patients with pulmonary hypertension. Deuchar and Knebel [4] estimated the distensibility of pulmonary arteries of young children by using an equation taken from Windkessel theory. Mean distensibility for children with normal pulmonary vascular dynamics was reported to be .7 ml/mm Hg by age 5, 1.1 ml/mm Hg at age 10, and 1.9 ml/mm Hg at age 20. By comparison, the mean distensibility for two children (age 7 yr) with atrial septal defects was 1.3 ml/mm Hg. Studying a much wider age range (5-40 yr), Shaw [23] used a fourelement model of the pulmonary circulation to estimate the normal distensibility of the pulmonary arterial system to be 3.1 ml/mm Hg and distensibility in septal defect patients to be 8.4 ml/mm Hg. Using the same theory as Engleberg and DuBois, Reuben [21] found an average compliance of 2.87 ml/mm Hg in patients with normal pulmonary pressure; values as low as 0.7 ml/mm Hg were found in patients with severe pulmonary hypertension. If the implications of these findings are correct, i.e., compliance tends to be lower in children
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than in adults, but higher in normotensive ASD patients than in patients with normal pulmonary pressures and flows, the mean preclosure estimate of compliance, 4.3 ml/ mm Hg,X obtained by using the threesegment transmission line model seems reasonable. The representative impedance modulus versus frequency curve predicted by this model showed smaller amplitudes fluctuations than those of other models [2, 3, 22, 241. This relatively flat configuration, however, compares favorably with the input impedance spectrum versus frequency data of Milnor et al. [18]. In that study of 10 human subjects (age range 21-38 yr), the pulmonary input impedance modulus fell sharply from relatively high values at 0 frequency to a minimum between 2 and 5 cycles/set and showed only small oscillations at frequencies above this minimum. Since such a model is probably more valuable for determining the direction of change in parameters than in determining accurate estimates of these parameter values, the sensitivity of the model to changes in the arterial and microcirculatory parameters in the neighborhood of the mean values given in Table 6 was examined. The broken lines in Figs. 6 and 7 show graphically the results of these analyses. For each parameter, the decreasescorrespond to 14 M, and x the original values; the increases correspond to fi 2, and 4 times the original values. Changes in A, (Fig. 6a) do not affect the frequency of the modulus minima and maxima, but markedly alter the range of the fluctuation. Decreasing AR results in larger fluctuations in both modulus and phase angle graphs. Increasing A, flattens modulus and phase angle graphs, increasing and making less obvious the first minimum modulus value which would remain at approximately 2 Hz. Small changes in A, have the most dramatic effect on the model (Fig. 6b). De*From Table 6: (3.20 x 10-3cmg/dyne) 103dyne/cm*/mm Hg) = 4.3 ml/mm Hg.
x (I.33 x
LUCAS, WILCOX AND COULTER: ATRIAL
SEF’TAL DEFECT CLOSURE
Frequency
(Hz)
FIG. 6. Sensitivity of input impedance spectrum of three-segment transmission line model to changes in arterial (A) resistance, (B) inertance, and (C) compliance. Solid line represents average spectrum shown in Fig. 5. For parameter decreases, broken lines correspond to I/&, l/2, and l/4 times the original parameter value (Table 6): for parameter increases, broken lines correspond to a 2, and 4 times the original value.
creasing A, raises the frequency but lowers the amplitude of the first modulus minimum; increasing A, has the reverse effect. Decreasing A, markedly raises both the frequency and amplitude of the first modulus maximum; the frequency of the first modulus
minimum is relatively unchanged, though the amplitude increases. Increasing A, (Fig. 6c) lowers both frequency and amplitude of modulus minima and maxima. Figure 7 shows the similarity in the spectrum response to inverse changes in MR and
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---
Before Atrlal Soptal Dwmarr in
Dhct
in MR
Clown
B. F
200
0 0 G=j 3.14 c c 1.57 a2 0 o u -LB8 8 s -3.14 0’
Frequency
(Hz)
FIG. 7. Sensitivity of input impedance spectrum of three-segment transmission line model to changes in microcirculatory (A) resistance and (B) compliance. Computational procedure same as in Fig. 6.
Mc. Decreasing MR or increasing Mc lowers the frequency at which the first modulus minimum occurs: changes in A4c are more discernible, especially at frequencies lower than 2 Hz. Likewise, increasing MR and decreasing Me have similar effects: the frequency of the first modulus minimum is slightly higher; however, the increase in MR tends to lower the value of that minimum while the decrease in Mc shifts the same value. The sensitivity analysis of the parameters emphasizes the importance of considering phase angle as well as modulus values when determining the frequency of the first minimum modulus value. The flat modulus values and the negative flat phase values
of patient 2 before closure (Figs. I and 4a) make determination of the frequency of the first minimum difficult. A relatively high value of A, was needed to fit such a configuration. However, a small decrease in the value of A, determined by the curve-fitting procedure produces a decrease in the modulus value at approximately 2 Hz, indicating that the first local minimum value occurs at 2 Hz rather than 6 Hz where the first measured minimum is located. The same situation could be the case for patient 4 after defect closure. However, the zero crossing of the phase curve at approximately 5 Hz indicates that the actual first minimum value is probably in the neighborhood of the minimum value measured at 6Hz.
LUCAS,
-3 l4C
WILCOX
AND
COULTER:
ATRIAL
SEPTAL
DEFECT
CLOSURE
583
I$+---2
4
6
a
IO
12
2
4
6
a
IO
12
FIG. 8. Changes in the pulmonary vascular input impedance spectrum in response to atrial septal defect closure predicted by selective changes in parameter values of the three-segment transmission line model. Solid line represents average preclosure spectrum shown in Fig. 5. Broken lines represent postclosure spectra computed as follows. (A) Postclosure differential vascular resistance same percentage distribution between arterial, microcirculatory, and venous segments as preclosure values; (B) total increase in differential pulmonary vascular resistance distributed in microcirculatory segment; (C) model parameter values equal to mean postclosure values given in Table 6.
Postclosure venous parameter values were calculated according to the criteria already given. The terminal impedance was changed to reflect the postclosure ratio of mean venous pressure to mean blood flow. Since there was a measurable increase in differential vascular resistance, the plausible distribution of that increase was first examined. The broken line in Fig. 8a shows the representative impedance spectrum that would be the result of a uniform increase in all segments, i.e., A,, M,, and VR are the same percentage of differential vascular resistance both before and after defect correction. Obviously, this does not agree with the direction of change observed in the actual impedance spectra.
A more satisfactory approach, shown in Fig. 8b, is to assume that all the increase is in the microcirculatory segment. The changes are slight but in the observed direction for most of the patient data: the frequency of the first modulus minimum is higher, the value of that minimum is slightly smaller, and the phase angle around 2 Hz is more negative. However, even a large change in M, would not account for the magnitude of the changes observed in the phase angle graphs of many of the patients. Using initial parameter values computed by the manner illustrated in Fig. 8b, the curve-fitting procedure was repeated for the postclosure impedance data. Except for matching the large positive phase angle value
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of patient 6 at 2 Hz, the curve-fitting criteria were met and the results are included in Table 6 and illustrated by the broken line in Fig, 8c. Comparison shows that the mean values for A,, A,, and AL decreased. The decrease in A, and A, raised the frequency of the first modulus minimum; the decrease in A, was primarily responsible for lowering the value of that minimum. The procedure was designed to change the value of A, only when realistic changes in other parameters could not obtain the desired results. The decreasemade was often necessary for fitting the more negative phase angle values often observed at 2 Hz. Neither an increase nor a decrease in A, had that effect: increasing A, did not have the desired effect on the modulus curve. Assuming the parameter changes predicted by the curve-fitting procedure are correct, two possible explanations of our findings present themselves for consideration. The first is that the major reflection site, or the juncture of the proposed arterial versus microcirculatory segment, is more proximal as a result of defect closure; hence, total resistance, inertance, and compliance would then be less in the shortened “arterial segment” even if the properties of that proximal segment remained the same.The second explanation is to assume that the three segments of the model continue to correspond to the same divisions of the vasculature, but undergo changesin size and wall properties. In anatomical terms, this possibly corresponds to increased radii of larger arterial vesselssince inertance beyond the 5th or 6th generations of arteries is already negligible, stiffening of the proximal arterial segment, and vasoconstriction or variations in the number and positions of microcirculatory vessels that are perfused. Interestingly, this response is almost identical to the response of the impedance spectrum to serotonin infusion modeled by Pollack et al. 1201. SUMMARY Results related to mean pressure and flow measurements were in the anticipated direc-
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tion. Pulmonary blood flow described as a result of defect closure and pulmonary pressures, in the normal range before closure, tended to remain the same; hence, the external work of the right heart decreased significantly. Changes in the differential pulmonary vascular resistance and the impedance spectrum indicated that there was an immediate pulmonary vascular response to defect closure. After closure, the differential pulmonary vascular resistance tended to increase, the frequency of the first minimum value of the impedance modulus curve tended to be higher, and the absolute value of the phase angle of the first harmonic tended to be larger. Analysis using a threesegment transmission line model suggests that closure of atria1 septal defects results in changes in the pulmonary circulation characterized by either (1) changes in the major reflection’ site or (2) dilatation and stiffening of proximal arterial vessels accompanied by vasoconstriction or decreased number of microcirculatory vesselsperfused. The parameters of the model are also being computed for a group of adult patients with atria1 septal defects and a group of normotensive children with ventricular septal defects. Comparisons of the parameter values and/or changes in the parameter values as a result of defect correction in these patients may offer additional insight into causes of the changes observed in the impedance spectra as a result of defect closure. APPENDIX I Equations Describing the Transmission Line Model Each segment of the transmission line model is assumed to be uniform and to be characterized by four constant (frequency independent) parameters: R = resistance per unit length; L = inertance per unit length; C = compliance per unit length; D = length of segment. Associated with each segment are four characteristic quantities obtained from standard transmission line theory [7]:
LUCAS. WILCOX AND COULTER: ATRIAL
1. The characteristic impedance Z,,, z, = ((R +jwL)/jwC)“2,
Q
585
SEPTAL DEFECT CLOSURE
=
Qp
‘p e-~* + “,
(1)
1
‘p Eve. 0
(9)
where w = angular frequency, j = fl
If the input impedance of each segment is the only quantity of interest, it can be y = CjwC(R + jwL))‘j2 shown that D can be eliminated as an inde(2) pendent variable and the equations simpli= M,e@ 7 = a + j@, fied by defining where M, = modulus;’ Br = phase angle; R, = RD. (10) (Y = attenuation per unit length; /3 = phase shift per unit length. L, = LD. (11) 3. The reflection coefficient, given by C, = CD. (12) 2. The complex wave number y, given by
r = -z, - ei is, + z,’
(3)
Then
where Z,, = terminal impedance of segment, which is equal to the input impedance of where the ensuing segment. 4. The input impedance of asegment Z,, given by z = z 1 - Ie-2rD 0 P 1 + Iee2TD = 1Z, 1,ej@= 24+ jv,
(4)
where u = hydraulic resistance; v = hydraulic reactance. The instantaneous values of pressure and flow, p and q, may be expressed in terms of their complex amplitudes, P and Q: p = Real(Pej”‘]. q = ReallQej”‘).
=
PP -.
Qp
O)
(6)
(7)
At any distance x from the proximal end of the segment, the complex amplitudes for the pressure and flow are P = Pp
zp+ zoemv*+ 22,
(13)
Z. =((RT + joLT)/jwCT)1/2
(14)
-yT = yD = (juC,(R,
+ jwLT))1/2.(15)
Calculation begins by assuming the terminal impedance of the venous segment to be a pure resistance equal to mean venous pressure divided by mean pulmonary blood flow. ACKNOWLEDGMENTS The authors express their appreciation to Nancy Wooten, Frank Boone, and Carol Porter for their assistancein this work.
REFERENCES
Hence, if the pressure (P,) and flow (Q,) at the proximal end of the segment are known, the input impedance can also be computed as zp
z = z 1 - IeSZYT 0 P 1 + Fe-2yT’
1
zp - zo evx 22, ’
(8)
1. Brody, J. S., Stemmler, E. J., and Dubois, A. B. Longitudinal distribution of vascular resistance in the pulmonary arteries, capillaries, and veins. J. Clin. Invest. 47783-199, 1968. 2. Caro, C. G., and McDonald, D. A. The relation of pulsatile pressure and flow- in the pulmonary vascular bed. J. Physiol. 157:426453, 1961. 3. dePater, L. An electrical analogue of the human circulatory system. Ph.D. Dissertation, University of Groningen, Netherlands, 1966. 4. Deuchar, D. C., and Knebel, R. The pulmonary and systemic circulations in congenital heart disease. bit.
Heart J. 14:225-249, 1952.
5 Engelberg, J., and Dubois, A. B. Mechanics of pulmonary circulation in isolated rabbit lungs. Amer. J. Physiol. 1%:401-414, 1959.
6. Glazier, J. B., Hughes, J. M. B., Maloney, J. E., and West, J. B. Measurements of capillary dimensions and blood volume in rapidly frozen lungs. J. Appl. Physiol. 26:65-16, 1969.
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7. Goldman, S. Luplace Transform Theory and Electrical Transients. Dover Pub., New York: 1966. 8. Heath, D., and Edwards, J. E., The pathology of hypertensive pulmonary vascular disease:A description of six grades of structural changes in the pulmonary arteries with special reference to congenital cardiac septal defects. Circulation l&533537, 1958. 9. Heath, D., Helmholz, H. F., Jr., Burchell, H. B., Dushane, J. W., and Edwards, J. E. Graded pulmonary vascular changes and hemodynamic findings in cases of atrial and ventricular septal defect and patent ductus arteriosus. Circulation
19:467-480, 1966. IS. Milnor, W. R., Conti, C. R., Lewis, K.
B., O’Rourke, M. F. Pulmonary arterial pulse wave velocity and impedance in man. Circ. Res. 25:627649, 1969.
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10. Heath, D., Helmholz, H. F., Jr., Burchell, H. B., Dushane, J. W., and Edwards, J. E. Relation be tween structural changes in the small pulmonary arteries and the immediate reversibility of pulmonary hypertension following closure of ventricular and atria1 septal defects. Circulation 18:1167-l 174, 1958.
11. Heath, D., Wood, E. H., Dushane, J. W., and Edwards, J. E. The structure of the pulmonary trunk at different ages and in cases of pulmonary hypertension and pulmonary stenosis. J. Parhol. Bacterial 77:443-456,
Dissertation, University of North Carolina, Chapel Hill, North Carolina, 1973. 16. McGoon, D. C., Swan, J. H. C., Brandenburg, R. O., Connolly, D. C., and Kirklin, J. W. Atria1 Septal Defect: Factors Affecting the Surgical Mortality Rate. Circulation 19:195-200, 1959. 17. Milnor, W. R., Bergel, D. H., and Bargainer, J. D. Hydraulic power associated with pulmonary blood flow and its relation to heart rate. Circ. Res.
1959.
12. Heath, D., Wood, E. H., Dushane, J. W., and Edwards, J. E. The relation of age and blood pressure to atheroma of the pulmonary arteries and thoracic aorta in congenital heart disease. Lab. Invest. 9~259-272, 1960.
13. Honda, T., Horiuchi, T. A., Koyamada, K., Ishitoya, T., and Ishizawa, E. Histometrical study of the pulmonary arteries in normal postnatal development and in patients with ventricular septal defect. Tohoku J. Exp. Med. 102:403-412, 1970. 14. Jarmakani, J. M. M., Graham, T. P., Jr., Benson, D. W., Jr., Canent, R. V., Jr., and Greenfield, J. W., Jr. In vivo pressure-radius relationships of the pulmonary artery of children with congenital heart disease. Circulation 43:585-592, 1971. 15. Lucas, C. Pulmonary input impedance spectrum of children with atria1 and ventricular septal defects: A computer simulation study based on a three segment transmission line model. Ph.D.
19. Patel, D. J., Defreitas, F. M., and Fry, D. L. Hydraulic input impedance to aorta and pulmonary artery in dogs. J. Appl. Physiol. 18:134-139, 1963. 20. Pollack, G. H., Reddy, R. V., and Noordergraaf,
A. Input impedance, wave travel, and reflections in the human pulmonary arterial tree: Studies using an electrical analog. IEEE Trans. Bio-Med. Eng. BME 15:151-164, 1968. 21. Reuben, S..R. Compliance of the human pulmonary arteriat system in disease. Circu. Res. 29:4050,1971. 22. Rideout, V. C., and Katra, J. A. Computer simu-
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