Longitudinal impedance is independent of outflow resistance.

Abstract

Many investigators have measured outflow resistance (R) following peripheral bypass procedures, but correlations with graft patency have been weak. This is because the primary determinants of graft patency are the size and quality of the conduit, not its outflow bed. Efforts at separating conduit resistance from outflow resistance have been unsuccessful. Recently, the concept of longitudinal impedance ( integral Z(L)) has been suggested as a measure of conduit resistance independent of outflow resistance. The purpose of this in vitro experiment was to test the hypothesis that integral Z(L) is independent of R within physiologically relevant ranges.
Rigid polyethylene tubing of known internal diameter and length (4.3 mm, 375 cm) was perfused with a glycerin/saline mixture mimicking the viscosity of blood (4.1 cp), utilizing a variable pulsatile pump and Windkessel, with outflow into multiply branched tubes of decreasing diameter simulating the hemodynamic conditions of arterial bypass. Flow and pressure were measured using ultrasonic transit time and catheter transduction, respectively, and waveforms digitized at 200 Hz. Flow was varied while maintaining "systemic" pressure and resistance. After Fourier transformation, integral Z(L) was calculated as deltaP/Q at each harmonic and integrated over 4 Hz.
integral Z(L) calculations were remarkably reproducible within the same day with a coefficient of variation (CV) = 4.0% (at 100 dyne. s/cm(5); n = 4) or over 4 successive days (CV = 4.3%). Furthermore, integral Z(L) was largely independent of R over the physiologic range tested, with integral Z(L) remaining relatively constant as R was increased sixfold.
integral Z(L) is a consistent and reproducible measure of conduit resistance independent of R over a wide physiologic range. It may be useful for measuring the adequacy of bypass graft conduits.

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Longitudinal Impedance Is Independent of Outflow Resistance
Michael A. Curi, M.D., M.P.A., Christopher L. Skelly, M.D., Clay Quint, B.S., Shari L. Meyerson, M.D.,
Amy J . Farmer, M.D., Umar M. Shakur, B.S., Francis Loth, Ph.D.,* and Lewis B. Schwartz, M.D.
Section of Vascular Surgery, University of Chicago, Chicago, Illinois 60637; and *Department of Mechanical and Industrial Engineering
and Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois 60637
Submitted for publication November 2, 2001
Background. Many investigators have measured
outflow resistance (R ) following peripheral bypass
procedures, but correlations with graft patency have
been weak. T his is because the primary determinants
of graft patency are the size and quality of the conduit,
not its outflow bed. E fforts at separating conduit resis-
tance from outflow resistance have been unsuccessful.
R ecently, the concept of longitudinal impedance (?ZL)
has been suggested as a measure of conduit resistance
independent of outflow resistance. T he purpose of this
in vitro experiment was to test the hypothesis that ?ZL
is independent of R within physiologically relevant
ranges.
Methods. R igid polyethylene tubing of known inter-
nal diameter and length (4.3 mm, 375 cm) was perfused
with a glycerin/saline mixture mimicking the viscosity
of blood (4.1 cp), utilizing a variable pulsatile pump
and Windkessel, with outflow into multiply branched
tubes of decreasing diameter simulating the hemody-
namic conditions of arterial bypass. F low and pres-
sure were measured using ultrasonic transit time and
catheter transduction, respectively, and waveforms
digitized at 200 Hz. F low was varied while maintaining
“systemic” pressure and resistance. After F ourier
transformation, ?ZL was calculated as ?P/Q at each
harmonic and integrated over 4 Hz.
R esults. ?ZLcalculations were remarkably reproduc-
ible within the same day with a coefficient of variation
(CV) ? 4.0% (at 100 dyne ? s/cm5; n ? 4) or over 4
successive days (CV ? 4.3%). F urthermore, ?ZL was
largely independent of R over the physiologic range
tested, with ?ZL remaining relatively constant as R
was increased sixfold.
Conclusion. ?ZLis a consistent and reproducible mea-
sure of conduit resistance independent of R over a wide
physiologic range. It may be useful for measuring the
adequacy of bypass graft conduits.
Key Words: longitudinal impedance; outflow resis-
tance; hemodynamics.
©2002 E lsevier Science (USA)
INTRODUCTION
The use of vein graft bypass for the treatment of
chronic arterial insufficiency has become common-
place. Although the procedure is initially successful in
almost all cases, the rate of vein graft failure after
vascular reconstruction remains high, with only 20–
50% of grafts remaining patent after 5 years. It has
been suggested that the most critical factors determin-
ing long-term patency are the choice of conduit, ade-
quacy of outflow, and technical performance of the
operation. While in general grafts with high flow fair
better than those with poor outflow, correlations of
outflow with graft patency have usually been weak
[1–8], and many grafts with very distal anastomoses
and diseased outflow may enjoy extended patency [4,
9]. A much stronger determinant of graft patency ap-
pears to be the size and quality of the conduit, not its
outflow bed. Hemodynamic characterization of the
“conduit only,” independent of its outflow bed, has been
elusive, however, and nogenerally accepted method for
measuring conduit resistance exists.
The concept of longitudinal impedance (?ZL) was
first described in the 1960s and characterizes the rela-
tionship between the pressure gradient and the flow
within a given length and type of rigid tubing. As this
concept contributes little to the understanding of flow
through compliant, branched arterial systems, it has
received minimal attention from arterial physiologists.
However, it is particularly well suited to the study of
long, unbranched, relatively rigid conduits that exhibit
high-pressure arterial flow patterns. Recently, ZL has
been examined as a putative measure of conduit resis-
Presented at the 25th World Congress of the International Society
of Cardiovascular Surgery, Cancun, September 12, 2001.
J ournal of Surgical Research 108, 191–197 (2002)
doi:10.1006/jsre.2002.6558
191
0022-4804/02 $35.00
© 2002 Elsevier Science (USA)
All rights reserved.

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tance independent of outflow resistance in the setting
of infrainguinal bypass grafting [10]. As the quotient of
the drop in pressure across the length of the conduit
and flow, ZL was shown to precisely assess vein graft
size and quality in vivo and was strongly correlated
with patency at 1 year. The results of this preliminary
study suggested that ZLmight be the elusive outflow-
independent hemodynamic measure of conduit resis-
tance that many investigators have sought. The pur-
pose of this experiment was to develop an in vitro
model of peripheral bypass grafting and use this model
to test the hypothesis that ?ZL is independent of out-
flow resistance (R) within physiologically relevant
ranges.
METHODS
Rigid polyethylene tubing of known internal diameter and length
(4.3 mm, 375 cm) was perfused with a glycerin/saline mixture mim-
icking the viscosity of blood (4.1 cp) with outflow into multiply
branched tubes of decreasing diameter simulating the hemodynamic
conditions of an arterial bypass. A variable-stroke pulsatile pump
was used to simulate rhythmic ventricular contraction. A Windkes-
sel (inline reservoir) was used to soften the up and down strokes
generated by the pump, yielding pressure and flow waveforms mim-
icking human arterial physiology. Proximal and distal pressure was
F IG. 1.
system.
Raw data obtained from continuous pulsatile in vitro
F IG. 2.
Note graphical representation of proximal and distal pressure (left), pressure gradient (middle), and blood flow (right).
Composite waveforms obtained from pulsatile in vitro system (A) and in a patient following infrainguinal bypass grafting (B).
F IG. 3.
integrated over 4 Hz. In this case, ?ZL ? 245 ? 103dyne/cm5.
Calculation of ?ZL. ZL is plotted against frequency and
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measured by fluid-filled catheter transduction. Flow through the
conduit was measured using ultrasonic transit-time flowmetry
(HT207; Transonics Systems, Inc., Ithaca, NY). Ten seconds of pres-
sure and flow waveform data were acquired digitally at 200 Hz.
According to the manufacturers’ specifications, pressure data were
accurate to within 12 mm Hg and flow data within 16 ml/min. Flow
was varied with mean from 70 to 250 ml/min (peak 315 ml/min)
while maintaining “systemic” pressure with mean of 100–150 mm
Hg (peak 177 mm Hg), yielding an R range of 50–250 ? 103dyne ?
s/cm5. These ranges were chosen to approximate clinical ranges for
infrainguinal bypass grafts [10, 11].
In vivo measurements of human vein graft flow and proximal and
distal pressure were obtained during a previously published study
[10]. In short, flow was measured by ultrasonic transit-time flow-
metry and pressure via fluid-filled 22-gauge catheter transduction.
Ten seconds of simultaneous pressure and flow data were acquired
digitally at 200 Hz.
The raw waveform data and calibration constants were imported
into a specially formatted, computer-aided design worksheet (Math-
CAD PLUS 6.0; MathSoft, Inc., Cambridge, MA). After acquisition of
each 10-s data set (Fig. 1), individual simulated heartbeats were
identified as points at which the flow waveform curve crossed a
preset threshold value equal to 80% of peak flow. The distance
between points was considered the length of a single simulated beat.
Individual beats were identified and separated, and any beats of
grossly different morphology were discarded. The remaining beats
were averaged to create a single composite flow waveform (Fig. 2).
The time-varying pressure gradient (?P) over the length of the graft
was calculated by the subtraction of the proximal and distal pres-
sure.
Data were subjected to Fourier transformation according to the
method of Nichols [12]. In short, the waveform is separated into a
series of simple sinusoidal waveforms of known frequency (har-
monic) and amplitude (modulus) that, when summed, approximates
the original waveform. Longitudinal impedance (ZL) was calculated
as ?P/Q at each harmonic and integrated over 4 Hz to yield a single
value of ?ZL (Fig. 3). Calculated values of ?ZL were analyzed for
reproducibility over a single day and over a successive 4-day period.
Coefficient of variation (CV) was calculated as (?/?) ? 100. The
relationship between ?ZL and R was examined using the method of
least-squares linear regression.
RESULTS
The morphology and magnitude of both outflow re-
sistance and ZL generated by the pulsatile pump and
Windkessel model were similar to those observed from
clinical measurements of infrainguinal bypass grafts
(Figs. 4 and 5). Calculated ?ZLwas remarkably repro-
ducible within the same day, with a CV of 4.0% (at 100
dyne ? s/cm5; n ? 4). Calculated ?ZLwas alsoreproduc-
ible over 4 successive days (CV ? 4.3%; Fig. 6).
As the outflow resistance was varied between 31 and
F IG. 4.
the qualitative similarities in both modulus (top) and phase angle (bottom). The 0th value of modulus is R.
Input impedance plots from pulsatile in vitro system (A, C) and in a patient following infrainguinal bypass grafting (B, D). Note
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191 ? 103dyne s/cm5, there was very little variation in
ZL at any of the first six harmonics, including the
zeroth (mean) (Fig. 7). Despite an increase in outflow
resistance of 600%, ?ZL remained relatively constant,
with a small nonlinear increase in ?ZL observed at
supraphysiologic levels of R (Fig. 8).
DISCUSSION
Ever since Alexis Carrel first described the use of
veins in arterial segments in 1906 [13], surgeons have
pondered the determinants of graft patency. Patient
characteristics and comorbidities [14–18], outflow re-
sistance [1, 2, 4, 6–9, 19], vein graft position [17, 20,
21] and direction [22, 23], flow, and velocity [24–33]
have all been championed as possible predictors of
patency. Although several methods have been devised
to measure the hemodynamic environment of outflow
[5–7, 34, 35], specific characterization of the hemody-
namic profile of the conduit has been elusive.
Such a specific measurement of conduit resistance
would by definition incorporate morphometry (both di-
ameter and length) as well as other potential mitigat-
ing graft properties such as wall thickness and compli-
ance, and it would also necessarily be independent of
the resistance generated by the outflow bed. Such a
parameter was initially described in the 1960s as the
electrical analog of longitudinal impedance(ZL), or the
relationship between pressure gradient and flow in a
given length of a rigid tube [36]. Until recently, this
measurement has had limited applicability as arterial
physiologists have traditionally been interested in
fluid flow through branched soft arteries, not rigid
unbranched tubes. However, ZLis ideal for the study of
grafts, as grafts are typically long, unbranched rigid
conduits, exhibiting high-pressure arterial flow pat-
terns.
In a recent study of a cohort of 73 infrainguinal vein
grafts, ZL was shown to significantly correlate with
1-year primary, primary-assisted, andsecondary patency
rates [10].In that study, ZLwas measuredunder baseline
F IG. 5.
similarities in both ZL modulus (top) and phase angle (bottom).
ZL plots from pulsatile in vitro system (A) and in a patient following infrainguinal bypass grafting (B). Note the qualitative
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and papaverine-stimulated (outflow-enhancing) condi-
tions. While the flow increased and outflow resistance
decreased markedly with the administration of papaver-
ine, ZL remained unchanged, suggesting its indepen-
denceof R. This practical finding correlates well with the
theoretical principles governing ZL[36].
The current study attempts to better delineate the
independence of ZL from R, by developing an in vitro
bench model that is consistent and easily reproducible.
The model closely simulates the hemodynamic envi-
ronment of vein grafts in vivo, incorporating a wide
range of physiologically relevant outflow conditions.
The results demonstrate that flow (Q), pressure gradi-
ent (?P), and input impedance are all essentially con-
strained by outflow resistance and are therefore inad-
equate indicators of conduit resistance. The quotient of
?P and Q, however, is independent of R, depending
only on the size and quality of the conduit. The simple
F IG. 7. Relationship of ZL vs R. The ZL curve remains fairly constant over a wide physiologic range of R.
F IG. 6. In vitro ZL measurement and calculation over a 4-day period. Note the constant values of ZL even at the higher frequencies.
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mathematical constant of ?P/Q using mean values is
notoriously difficult to calculate, given the imprecision
of measuring small mean pressure differences with
fluid-filled catheters. However, since large conduits
primarily provide resistance to fluid traveling in
pulses, their resistance is best measured using pulsa-
tile waveforms with separation of their components
using the mathematical techniques of Fourier. Indeed,
the conduit’s resistance to flow traveling at the funda-
mental frequency is actually higher than theresistance
to continuous flow. Thus the total resistance that the
conduit provides must be calculated from the full fre-
quency spectrum, lest it be grossly underestimated.
Incorporation of the first four harmonics was used in
this study, as in the clinical study [10], in order to
standardize the patient cohort and maximize the
signal-to-noise ratio. As the frequency increases, the
modulus of both ?P and Q decreases, thereby decreas-
ing the signal-to-noise to ratio; the ability to reliably
calculate ZLat very high harmonics is limited. There-
fore very high harmonics are not included in the cal-
culation of ?ZL.
?ZLremained relatively constant over an increase in
outflow resistance of 600%. This is what would be
expected for a measure of conduit-specific resistance.
The small increase seen at higher levels of outflow
resistance is probably a function of increasing impre-
cision at higher frequencies, also evident in the in-
creasing standard errors for calculated ?ZL(Fig. 8).
In summary, longitudinal impedance is a consistent
and reliable measure of conduit resistance, indepen-
dent of outflow resistance, and can be modeled effec-
tively in vitro. This measurement has previously been
shown tocorrelate well with patency of vein grafts and
lends support to the notion that the quality of the
conduit itself, rather than outflow resistance, is the
more important determinant of graft patency.
ACKNOWLEDGMENTS
Dr. Curi is supported in part by a Frederick A. Coller Society
Fellowship. Dr. Skelly is supported by Thoracic Surgery Research
Fellowship 99019, Thoracic Surgery Foundation. Dr. Meyerson is
supported by Cardiovascular Pathophysiology and Biochemistry
Training Grant NIH/NHLBI 5T32 HL07237. Dr. Schwartz is sup-
ported in part by AHA Scientist Development Grant 9930338Z.
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