Vol. 278, Issue 3, H998-H1007, March 2000
SPECIAL COMMUNICATION
A novel servo-control system that imposes desired aortic input
impedance on in situ rat heart
Hiroshi
Miyashita1,2,
Masaru
Sugimachi1,
Takayuki
Sato1,
Toru
Kawada1,
Toshiaki
Shishido1,
Tsutomu
Nakahara1,
Ryoichi
Yoshimura1,
Hiroshi
Takaki1,
Hiroshi
Miyano1, and
Kenji
Sunagawa1
1 Department of Cardiovascular Dynamics,
National Cardiovascular Center Research Institute, Suita, Osaka
565-8565; and 2 Department of
Physiology, Jichi Medical School, Minamikawachi-machi, Tochigi
329-0498, Japan
 |
ABSTRACT |
To
clarify the pathophysiological role of dynamic arterial properties in
cardiovascular diseases, we attempted to develop a new control system
that imposes desired aortic impedance on in situ rat left ventricle. In
38 anesthetized open-chest rats, ascending aortic pressure and flow
waveforms were continuously sampled (1,000 Hz). Desired flow waveforms
were calculated from measured aortic pressure waveforms and target
impedance. To minimize the difference between measured and desired
aortic flow waveforms, the computer generated commands to the
servo-pump, connected to a side branch of the aorta. By iterating the
process, we could successfully control aortic impedance in such a way
as to manipulate compliance and characteristic impedance between 60 and
160% of their respective native values. The error between desired and measured aortic flow waveforms was 70 ± 34 µl/s (root mean square; 4.4 ± 1.4% of peak flow), indicating reasonable accuracy in
controlling aortic impedance. This system enables us to examine the
importance of dynamic arterial properties independently of other
hemodynamic and neurohumoral factors in physiological and clinical settings.
pressure and flow waveforms; dynamic afterload; iterative control
algorithm; native aortic impedance
| |
INTRODUCTION |
CHANGES IN arterial pressure and flow waveforms are
known to result from various cardiovascular diseases, such as
hypertension, congestive heart failure, arteriosclerosis, aging, and
the application of vasoactive agents (10, 15, 18-20, 26). On the
other hand, several clinical and experimental studies have suggested
the importance of arterial pressure waveforms rather than mean arterial
pressure levels in the progression of cardiovascular disease. The
extent and eccentricity of left ventricular hypertrophy in rats induced by aortic constriction at different sites varied considerably even when
mean arterial pressure levels were similar (13). Antihypertensive agents that lower mean arterial pressure to the same degree did not
necessarily induce the same degree of regression of left ventricular hypertrophy (17). Some vasodilators were effective in decreasing mortality of patients with left ventricular dysfunction without significant changes in mean arterial pressure (14) but with changes in
the pressure waveform. The mean arterial pressure obviously cannot
account for these diverse outcomes, but the differences in arterial
pressure waveform might be a candidate for this diversity (1, 7) aside
from the difference in humoral factors and/or preload.
As ventricular volume changes during ejection, ventricular afterload as
assessed by wall stress should differ considerably among different
ejection patterns (i.e., ejection with different arterial pressure
waveforms). Furthermore, because the failing hearts are more
susceptible to changes in afterload (16, 26), the impact of different
pressure waveforms may be even larger in these weak hearts.
However, because of technical reasons, the clinical and
pathophysiological significance of dynamic arterial properties remains to be established. Techniques for selective manipulation of dynamic arterial properties have been limited. Pharmacological interventions (15, 18, 27) cannot substitute for selective manipulation given the
alterations in preload, ventricular contractility, heart rate, and
neurohumoral factors that inevitably accompany such treatment. Physical
interventions [aortic constriction (13), replacement of the aorta
with a stiff tube (11, 22)] used in previous studies were not
sufficiently versatile to impose arbitrary impedance on the ventricle.
The limited ex vivo experiments on impedance loading with hydraulic
load (5, 9, 25) or servo-pumps (2, 12, 24) have been more
versatile, but they were only able to impose impedance
based on a particular arterial system model such as windkessel (5, 9,
24, 25) or T-tube models (2, 12). No attempts to impose desired aortic
impedance on in situ heart have been reported. The aim of this study
was to develop an experimental device that imposes desired impedance on
the in situ left ventricle. The results indicate that desired impedance
was successfully imposed on the rat heart with a feedback iteration
algorithm and a high-fidelity servo-pump system.
| |
METHODS |
Principles of an operation for controlling impedance imposed on an in
situ heart.
Figure 1 shows the schema for our
manipulation of the impedance imposed on the in situ heart. We
connected the outlet of a piston pump to the side branch of the aorta
to allow for instantaneous addition or withdrawal of extra flow to the
native aortic flow. To control impedance, we first calculated the flow
required to achieve the target impedance from the measured pressure
waveform and the target impedance. We drove the piston pump according
to the difference between desired and measured flow waveforms. Because the activation of the piston pump alters aortic pressure waveform, we
repeated this cycle until the difference between desired and measured
flow waveforms disappeared.
View larger version (38K):
[in this window]
[in a new window]
|
Fig. 1.
Schematic illustrating impedance control in situ. The left ventricle
ejects blood into the native arterial system characterized by aortic
impedance [Zin(f)]. By moving
the servo-pump, we effectively imposed an artificial impedance
[Zpmp(f)] in parallel to
generate target impedance
[Zcmd(f)]. These impedance
values are related to each other by the formula
1/Zcmd(f) = 1/Zin(f) + 1/Zpmp(f). Specifically, desired flow
waveform [Fcmd(t)] is calculated using
aortic pressure waveform [PAo(t)] and
target impedance, and instantaneous pump flow
[Fpmp(t)] is determined so as to
gradually minimize the difference between Fcmd(t)
and measured aortic flow waveform
[FAo(t)].
|
|
Animal preparation and instruments.
Animal care was in accordance with institutional guidelines.
Thirty-eight adult male Sprague-Dawley rats (9-19 wk of age, 460 ± 91 g body wt) were anesthetized with intraperitoneal urethan (1.5 ± 0.3 g/kg). Artificial ventilation was performed via a
tracheotomy with oxygen-enriched room air at a rate of 65-80
breaths/min and a tidal volume of 3-4 ml. To eliminate autonomic
nerve reflexes, we used pithing (n = 16 animals) (6),
transection of the cervical spinal cord (n = 6 animals) (8), or
intravenous administration of hexamethonium (60 ± 44 mg/kg; n = 16 animals) in addition to bilateral vagotomy. Blood
pressure levels were maintained by continuous intravenous infusion of
methoxamine (15-30
µg · kg
1 · min1;
n = 9 animals) and/or blood transfusion (6.1 ± 2.7 ml;
n = 36 animals). After a median thoracotomy was performed, a
2-Fr catheter-tipped micromanometer (model SPC320, Millar Instruments,
Houston, TX) was introduced into the ascending aorta at the level of
the right brachiocephalic artery bifurcation, and an ultrasound
transit-time flow probe [inner diameter (ID) 2.5 mm; model 2.5SB,
Transonic Systems, Ithaca, NY] was placed around the ascending
aorta just proximal to the tip of the micromanometer. The
low-pass filter of the flowmeter was set at 100 Hz. We fixed heart rate
by either atrial pacing or sequential dual-chamber pacing with 10 ms of fixed atrioventricular delay.
The custom-designed servo-controlled piston-pump system (model ARB-126,
Air Brown, Osaka, Japan) consisted of a piston pump, a linear motor, a
displacement transducer, analog circuits, and a tube for connecting the
pump to the animal. The diameter of the piston pump was 25 mm, and the
pump had a stroke of 20 mm (23, 24). The piston was driven by a linear
motor (model ET-126A, with a power amplifier model PA-118, Labworks,
Costa Mesa, CA). Custom-made analog circuits controlled pump volume by
referencing to the position of the piston measured by a linear
displacement transducer. The outlet of the pump cylinder was connected
to the aorta via stainless steel tubing (ID 2 mm). An in-line flow
probe (model 2N, Transonic Systems) was placed between the distal end of the tubing and a plastic catheter [ID 0.8 mm, outer diameter (OD) 1.1 mm; model SR-OS2032, Terumo, Tokyo, Japan] inserted into the aorta via the left carotid artery. Detailed characteristics of the
system are described in the APPENDIX. The pump and the tube were filled with heparinized (20 U/ml) physiological saline. Special care was taken to completely remove air bubbles from the tubing. Pressure and flow waveforms were digitized at a sampling rate of 1 kHz
with the use of a 12-bit analog-to-digital converter [model
AD12-16D(98)H, Contec, Osaka, Japan] interfaced with a dedicated
laboratory computer system (PC-9821Af, NEC, Tokyo, Japan). These data
were sampled and averaged over several (typically 4-5) beats
corresponding to one ventilatory cycle to minimize the influence of
respiratory variations in pressure and flow.
Algorithm of the iterative feedback control.
As already stated in Principles of an operation for controlling
impedance imposed on an in situ heart, we manipulated the flow
waveform by driving the servo-pump. To accomplish this, we used an
iterative approach in which the imposed impedance gradually approached
the target impedance (Fig. 2). The target
impedance [Zcmd(f)] was
prepared a priori.
View larger version (28K):
[in this window]
[in a new window]
|
Fig. 2.
Algorithm for volume command calculation. Index n in
parentheses indicates variables for the nth iteration cycle;
index n  1 indicates variables given in the previous
iteration cycle. Symbols in circles are numerical operators, terms in
boxes are signals or characteristics, and terms in octagons are
procedures. Symbols and terms in filled circles and boxes represent
characteristics given in the frequency domain. FFT, fast Fourier
transform; IFFT, inverse FFT; FAo, measured aortic flow
waveform; Fcmd, desired aortic flow waveform;
Fpmp, instantaneous pump flow command; H, transfer
function of servo-pump system; K, weighting factor for flow
error correction; PAo, measured aortic pressure waveform;
Vcmd, pump volume command; Zcmd, target
impedance function.
|
|
We switched the command to drive the servo-pump every 8-10 beats,
which in turn was dependent on pacing rate, ventilation rate, and the
time period required for command calculation. In each iterative cycle,
we first measured aortic pressure
[PAo(t)] and flow
[FAo(t)] waveforms. Using a fast
Fourier transform (3), we calculated the amplitude and phase spectra of
pressure [PAo(f)]. We calculated the
desired instantaneous flow [Fcmd(f)] in
the frequency domain that should be ejected in response to the measured pressure waveform against the specified Zcmd(f) as
follows
Next, after converting the desired instantaneous flow to a
time-domain signal through the inverse Fourier transform, we calculated the optimal instantaneous error flow for manipulation by the servo-pump by subtracting measured flow waveform from desired flow waveform at
each time point within a cardiac cycle. We did not correct all of the
error flow values within a single iteration cycle; rather, we corrected
only a small fraction of the error (factor K in Fig. 2,
typically 5-10%) to avoid any instability in the control.
Finally, flow correction was added to the previous flow command,
converted to a volume command, modified to compensate for the
characteristics of the servo-pump system (see APPENDIX), and then applied to the pump. Time delay caused by pulse wave travel
over the distance between the end of the tube and the aortic root was
also taken into account.
Impedance based on the measured pressure and flow waveforms was
calculated on-line. Programs for impedance control, data acquisition, and impedance calculation were all custom developed using Microsoft Assembler and FORTRAN on MS-DOS on a dedicated laboratory computer system (PC-9821Af, 60-MHz Pentium, NEC).
Evaluation of impedance control accuracy.
To evaluate the accuracy of impedance control, we calculated the root
mean square of time-domain errors (RMSEt) between measured and desired aortic flow waveforms. We also calculated the
coefficient of determination (R2) between the two
flow waveforms. RMSEt relative to the root mean
square (RMS) of Fcmd was evaluated throughout the
experiments. We concluded that the iteration had reached convergence
(successful control) at RMSEt <15% of
RMS of Fcmd and R2 > 0.980. In the
final off-line analysis, RMSEt was also expressed
as a percentage of the peak value of Fcmd. We also examined various pressure values to express the changes in pressure waveforms by
impedance control. These include peak systolic pressure
(Ps), diastolic pressure (Pd), pulse pressure
(PP), and end-ejection pressure (Pee).
We evaluated the similarity in the impedance values by comparing the
measured and the target impedance by calculating the root mean square
of error for moduli
(RMSE|Z|) and for
phases (RMSE
). We assessed these errors over the frequency range of 
80 Hz. We also assessed these errors over the
frequency range of 26 Hz, a range that included the major power of
flow for each rat.
Figure 3A shows the power spectra
of aortic pressure and flow obtained in the preliminary experiments. On
average, 99% of the total alternating current power of
pressure and flow were within the frequency ranges <26.7 ± 3.0 Hz
(range 20.0-34.2 Hz) and <42.1 ± 9.6 Hz (range 26.4-65.9
Hz), respectively. We therefore decided to assess the precision of
impedance control at 26 Hz as stated above. The average impedance
obtained in these experiments is shown in Fig. 3B. Because
coherence values were >0.8 up to 80 Hz, we determined the frequency
band for impedance control up to 80-100 Hz. Total peripheral
resistance was 162 ± 39 mmHg · s · ml1,
characteristic impedance (ZC) was 11.4 ± 3.1 mmHg · s · ml1,
and windkessel compliance (C) was 1.08 ± 0.23 µl/mmHg (corner frequency 1.03 ± 0.23 Hz). The modulus of the impedance
corresponding to the first harmonic of normal heart rate (calculated as
the average between 5 and 7 Hz) was 18.3 ± 5.3 mmHg · s · ml1.
View larger version (28K):
[in this window]
[in a new window]
|
Fig. 3.
Characteristics of baseline native aortic pressure and flow waveforms
expressed in frequency domain. A: group-average power spectra
(+SD, dotted line) of aortic pressure (PAo) and flow
(FAo) signals. B: average (±SD, dotted lines)
impedance spectra with coherence function. All spectra were obtained
under random pacing and with multiple 2,048-point (2.048 s) segments.
Frequency resolution was 0.5 Hz.
|
|
Protocols and data analysis.
To calculate a reference for target impedance, we first obtained
high-resolution native aortic impedance (Fig. 3B). We needed high-resolution impedance because heart rate was not necessarily constant. High-resolution impedance was obtained through the use of
random pacing (R-R interval 200 ± 50 ms, range 26-354 ms) and ensembling of power to reduce spectral variance (4). We obtained an
impedance with a frequency resolution of 0.5 Hz.
We examined the ability of the servo-pump system to control
impedance. The protocols included selective changes in
ZC, rescaling of the frequency axis, and selective
changes in the first harmonic impedance (Z1). The
latter two protocols effectively modified arterial compliance (C), but
in different ways. They differed in whether the high-frequency range
was rescaled or not and in the behavior of the high-frequency
reflection wave. For all impedance modifications, we first defined the
modified impedance modulus as stated below and then determined the
phase according to the minimal phase condition using Hilbert transform
(21). The reference ZC value was defined as the
average modulus of the original impedance at 20-100 Hz. As Fig.
4A shows, ZC
was altered by offsetting impedance modulus uniformly, excluding direct
current (DC). Figure 4B shows how we rescaled the
frequency axis. We uniformly rescaled frequency axis throughout the
frequency range. Selective changes in Z1 (Fig. 4C) were achieved by scaling the impedance modulus according to the frequency of heart rate (~5 Hz). Around this frequency, the degree of scaling was smoothly tapered. We truncated the reciprocal of
target impedance above 80 Hz, where both pressure and flow power were
negligible.
View larger version (19K):
[in this window]
[in a new window]
|
Fig. 4.
Target impedance created by modifying native impedance.
A-C show modulus of native impedance
(Zin; dotted lines) and modulus of modified target
impedance (solid lines). A: characteristic impedance
(ZC) was modified. Compliance (C) was modified
either by rescaling frequency axis (B) or by changing the
modulus for the first harmonic of heart rate (Z1)
(C), respectively.
|
|
One of the target impedances was imposed for 2-3 min, which
included the transient phase of the impedance control (see example in
Fig. 5). Aortic pressure, aortic flow, and pump flow waveforms were
recorded, and aortic impedance was obtained on-line at baseline, during
steady state of each impedance control, and 1 min after the control was
stopped, when the effect of impedance control had subsided. We used the
mean values measured before and 1 min after impedance loading was
stopped as the baseline values and compared these with values measured
during the control. We performed several protocols using the same rat.
Given the nature of the piston pump, the inability to control DC
impedance (i.e., resistance) resulted in an inability to compensate for
changes in resistance of the native arterial system. To eliminate any
confounding factors arising from this deficit, we discarded any data in
which native arterial resistance changed more than 5%.
Statistical analysis.
Data are expressed as means ± SD. A paired t-test was used
for comparison between data at baseline and during impedance control in
the same rat. The accuracy of impedance control was compared among four
different protocols of impedance modification by one-way ANOVA with
Scheffé's post hoc procedure. A P value <0.05 was accepted as statistically significant.
| |
RESULTS |
Time course of impedance control.
Figure 5 presents a representative time
course of impedance control wherein a high ZC value
was obtained. Increasing PP indicated an increased
ZC value. Given the iterative nature of the
algorithm, the pump flow waveform was gradually altered to attain the
target impedance. PP was also gradually increased until it reached a final steady state. The time required to reach a steady state was
dependent on the correction factor (K), pacing rate, and the extent of discrepancy between native and target impedance values. With
larger values of K, we were able to reach a steady state with
fewer iteration processes at the expense of instability (data not shown). Steady state was usually attained within a few minutes with
K values between 0.03 and 0.1.
View larger version (41K):
[in this window]
[in a new window]
|
Fig. 5.
Time course of impedance control. A representative time course of
measured PAo, FAo, and Fpmp
waveforms during impedance control is shown. Detailed waveforms for
every 10 s were superimposed. ZC was increased by
impedance control. Pulse pressure was gradually increased, accompanied
by an increase in amplitude of Fpmp. Steady state was
reached within 1 min in this case.
|
|
Changes in waveforms and imposed impedance by impedance control.
Figure 6A shows changes in
waveforms and changes in impedance imposed by doubling
ZC. Before the impedance control reached steady
state, large differences were observed between measured (FAo) and desired (Fcmd) flow waveforms (Fig.
6A, baseline). Measured impedance was not close to the target
impedance. Once the impedance control reached a steady state (Fig.
6A, Zin load), the differences between the
measured and desired flow waveforms were greatly attenuated. Measured
impedance coincided reasonably well with the target impedance up to at
least 35 Hz in the example in Fig. 6. RMSEt decreased by 84%,
RMSE|Z| (<26
Hz) decreased by 50%, and RMSE (<26 Hz) decreased by
80%. Impedance did not necessarily agree with the target above 40 Hz.
Note that desired flow waveform was not the same between time points
before and after the impedance control had reached a steady state. This
is because the altered impedance affected the pressure waveform, which
in turn altered the desired flow waveform. When ZC
was doubled, Ps increased by 5.5 mmHg, Pd
decreased by 0.6 mmHg, and, as a result, PP increased by 6.1 mmHg.
Pee was decreased by 8.3 mmHg.
View larger version (48K):
[in this window]
[in a new window]
|
Fig. 6.
Changes in impedance and waveforms with impedance control
(Zin load) in representative cases. A:
ZC was increased; B: ZC
was decreased; C: C was decreased; D: C was increased.
A-D: moduli and phases of target (lines) and measured
impedance ( )are shown at baseline and Zin load.
Measured impedance was obtained only for discrete frequencies because
it was obtained from a single beat. Measured pressure (PAo,
thick lines) and flow waveforms (FAo, thin lines; desired
Fcmd, dotted lines) are shown as well as instantaneous pump
flow command (Fpmp).
|
|
Figure 6B depicts the changes in waveforms and impedance
imposed by halving ZC. RMSEt,
RMSE|Z|, and
RMSE decreased by 74%, 61%, and 87%, respectively.
Ps decreased by 5.9 mmHg, Pd decreased by 2.5 mmHg, and, as a result, PP decreased by 3.4 mmHg. Pee was
decreased by 1.5 mmHg. In Fig. 6C, changes in waveforms and
impedance imposed by halving C are shown. RMSEt,
RMSE|Z|, and
RMSE decreased by 69%, 67%, and 76%, respectively.
Ps decreased by 0.3 mmHg, Pd decreased by 9.1 mmHg, and, as a result, PP increased by 8.8 mmHg. Pee was
increased by 3.5 mmHg, and diastolic decay became steeper. In Fig.
6D, changes in waveforms and impedance imposed by an increase
in C of 60% are shown. RMSEt, RMSE|Z|, and
RMSE decreased by 89%, 83%, and 79%, respectively.
Ps increased by 2.7 mmHg, Pd increased by 7.6 mmHg, and, as a result, PP decreased by 5.0 mmHg. Pee was decreased by 7.1 mmHg, and diastolic decay became less steep.
By both increasing ZC and decreasing C (by either
rescaling frequency or increasing Z1), PP increased
as a result of lowered Pd with a minimal effect on
Ps. These two parameters differed in that in response to a
high ZC, the onset of ejection was induced to occur
earlier and the pressure upstroke to become steeper to a greater extent
than was induced by a low C. In response to a high
ZC but not a low C, Pee decreased and
ejection time was prolonged. In response to a low C, the pressure peak
was delayed and Pee increased. The effects of decreasing
ZC and increasing C were basically the opposite of
those of increasing ZC and decreasing C, respectively.
Accuracy and controllability of the impedance control system.
Figure 7 shows the changes in error indexes
imposed by impedance control. In 138 experiments,
RMSEt was markedly reduced from 262 ± 124 to 70 ± 34 µl/s (P < 0.001) after impedance control was
imposed, which corresponded to 16.9 ± 5.3% and 4.4 ± 1.4% of peak
Fcmd before and after impedance control, respectively. The
correlation coefficient between the measured and the desired flow
waveforms nearly approached unity (R2 from 0.884 ± 0.087 to 0.988 ± 0.010). Reductions in
RMSE|Z| and
RMSE by impedance control were modest when evaluated over the frequency range of 80 Hz
(RMSE|Z| from
11.3 ± 6.7 to 8.5 ± 10.4 mmHg · s · ml1,
P = 0.026; RMSE from 0.49 ± 0.18 to
0.33 ± 0.19 radians, P < 0.001). When evaluated within the
limited bandwidth (26 Hz) in which the majority of power of flow
signals were found (Fig. 3A), reductions were larger and
comparable with those evaluated in the time domain
(RMSE|Z| from 9.4 ± 4.9 to 4.0 ± 2.5 mmHg · s · ml1,
P < 0.001; RMSE from 0.32 ± 0.15 to 0.13 ± 0.07 radians, P < 0.001).
View larger version (22K):
[in this window]
[in a new window]
|
Fig. 7.
Effects of impedance control on time- and frequency-domain error
variables. Values at baseline (B) and during impedance control (Z load)
are compared. A: time-domain error variables, i.e., root mean
square of errors (RMSEt) and coefficient of
determination (R2) between measured and desired
aortic flow waveforms. B and C: frequency-domain error
variables, i.e., RMSE between measured and target impedance moduli
(RMSE|Z|)
(B) and that between measured and target impedance phases
(RMSE) (C). In each panel, errors
(RMSE|Z| or
RMSE) evaluated at <80 Hz and <26 Hz (bandwidth
within which most flow power resides) are shown side by side. Error
bars represent 1 SD. *P < 0.05;  P < 0.001 vs.
baseline.
|
|
Figure 8 shows a comparison of the error
indexes among different protocols. The correlation coefficients between
the measured and desired flow waveforms were comparable. Although
RMSEt was larger in the low-ZC
group than in the high-ZC and low-C groups, these
differences were not evident when we normalized
RMSEt by peak Fcmd.
RMSE|Z| and
RMSE (evaluated <80 Hz) varied too greatly among
animals to allow detection of differences between protocols. Limiting
the frequency range (<26 Hz) reduced the interanimal variance and
enabled detection of differences.
RMSE|Z| was
larger in the high-ZC group than in the low-C and
high-C groups, whereas RMSE was larger in the
high-ZC group than in the low-C group.
View larger version (29K):
[in this window]
[in a new window]
|
Fig. 8.
Comparison of time- and frequency-domain error variables among
different impedance control protocols after impedance control reached a
steady state. HZC, LZC, HC, and
LC denote protocols that increase (high) and decrease (low)
characteristic impedance and compliance, respectively. A:
R2 between measured and desired flow waveforms.
B: RMSEt between measured and desired
aortic flow waveforms evaluated in time domain is shown with error
normalized by peak desired flow (Fcmd) value
(%RMSEt).
RMSE|Z|
(C) and RMSE (D) in frequency domain are
also shown. In each panel, variables are evaluated over the 2 different
ranges of frequency, <80 Hz and <26 Hz (bandwidth within which most
flow power resides). Error bars represent 1 SD. *P < 0.05;
P < 0.01 between protocols.
|
|
As shown in METHODS, we defined successful control as
RMSEt <15% of the RMS of Fcmd and
R2 
0.98. In addition, we empirically determined
and fixed the weighting factor for flow error correction (K)
between 0.05 and 0.1, because these values are acceptable in terms of
stability and speed of convergence. The time delay between the aortic
root and the catheter tip (2-3 cm) was fixed at 4 or 5 ms, on the
basis of preliminary measurements.
On average, ZC could be successfully modified
between 60 and 160% of control, whereas modification of C by frequency
rescaling was successful between 50 and 300% of control. With
Z1 modification, 50 and 200% of the native value
were demonstrated to be the limits of successful control. Quality of
impedance control appeared to depend on the native cardiac output as
well as the difference between target and measured impedance, because
these are the major determinants of pump flow. Maximal pump ejection
appeared to be the limiting factor for these controls.
| |
DISCUSSION |
We developed a servo-control system that imposes the desired impedance
on the in situ rat left ventricle. The system consisted of a specially
tuned piston pump, a linear motor, analog servo-feedback circuits, and
an iteration control algorithm. This system was capable of controlling
the dynamic components of aortic impedance and therefore enabled the
reproduction of aortic pressure and/or flow waveforms or left
ventricular afterload conditions in actual cardiovascular disease
(e.g., arteriosclerosis, congestive heart failure, hypertension, and
aging) independently of neurohumoral factors.
Advantages of our methods.
Only a few reports on artificial impedance loading experiments in
hearts can be found. These are divided into two types of experiments,
physical manipulation of native outflow and ejection against the
hydraulic afterload or controlled piston pump. In an in situ dog
experiment, Randall et al. (22) and Kelly et al. (11) imposed increased
pulsatile load by replacing the native aorta with a stiff tube.
Kobayashi et al. (13) reported that they produced chronic hypertensive
rat models with different aortic impedance by imposing aortic
constriction at different sites. These physical manipulations did not
show versatility and precision in controlling impedance. Elzinga and
Westerhof (5) and Ishide et al. (9) utilized a hydraulic model of
modified windkessel to simulate aortic impedance in dogs. Sunagawa et
al. (24) first introduced computer-based impedance control using a
modified windkessel model for real-time loading on isolated canine
hearts. Kirkpatrick et al. (12) and Berger et al. (2) imposed impedance
based on somewhat complicated models (asymmetric T-tube model and
single elastic tube model, respectively). Although these methods were more versatile and precise in controlling impedance, only impedance based on a particular model can be loaded. Furthermore, the condition of the heart in these ex vivo experiments was far from approximating physiological conditions.
Burkhoff et al. (4) showed that a modified windkessel model reproduces
natural impedance in that it produces similar mean pressure and stroke
volume. However, the pressure and flow waveforms associated with the
model are quite different from those observed in animals. The
difference between the model and natural impedance becomes evident when
we examine the impulse response (time-domain representation) of
impedance. We succeeded in loading modified impedance, based on natural
impedance, with a method that was capable of producing more realistic
pressure and flow waveforms. In addition, our method is, at least in
principle, more versatile given that we can load impedance that is not
limited to modified natural impedance within the performance limits of
the pump.
Other advantages of our method include the fact that it does not
require knowledge of native impedance a priori or any surgical procedure on the native artery itself, the latter of which enables the
easy reestablishment of the control condition.
Iterative nature of the algorithm.
Because of the iterative nature of the algorithm, it takes time to
reach a steady state of impedance control. Because aortic pressure and
flow waveforms gradually approached desired shapes, hemodynamic
stability (including natural aortic impedance) was required during this
transient phase. Indeed, when frequent irregular beats were noted, this
algorithm did not work. This gradual manner of control was not
necessarily disadvantageous. It might be preferable for the in situ
condition given that the native circulatory system might never
experience such an abrupt change in impedance. Although autonomic nerve
reflexes were blocked in this study, homeometric and/or heterometric
autoregulation of left ventricular ejection and flow-dependent
vasodilation were allowed to occur during this phase.
Effect of impedance on pressure and flow waveforms.
Essentially, ZC is characterized as impedance
modulus for higher frequency, whereas C relates to impedance for lower
frequency. Thus increased ZC was expected to induce
augmentation of pressure for the upstroke and early ejection phases.
Lower C, which increases impedance at lower frequencies, should augment
pressure in late systole and at end ejection. Observed waveform changes
during the impedance control were consistent with these expected changes.
Comparison of accuracy of control in the time and frequency domains.
RMSEt between desired and measured aortic flow
waveforms of <5% of peak desired flow and R2 of
>0.98 with a small variance were indicative of excellent accuracy of
impedance control when expressed in the time domain. Desired and
measured flow waveforms were nearly superimposable. Compared with this
high level of accuracy in the time domain, the accuracy in the
frequency domain appeared somewhat lower when evaluated over the
frequency range of 80 Hz. If the frequency range for calculation of
RMSE|Z| and
RMSE was limited to 26 Hz, the accuracy and its
variance became comparable with those in the time domain. Therefore,
the discrepancy between these indexes of accuracy in the time and
frequency domains is likely due to the fact that more power is present
for lower-frequency components. Because we intentionally controlled
flow waveform on the basis of the time sequence of error signals, a
simple (nonweighed) average of errors in the frequency domain may have
magnified the error in the high-frequency range. The observed
superiority in controlling C rather than ZC in the
frequency domain (but with equivalent accuracy in the time domain)
might also have been attributable to the same phenomenon. Variabilities
that have arisen from the estimation of impedance based on a single
beat might be included. On the basis of these findings, for our
purposes we judged that precision in the time domain is more important
than that in the frequency domain.
Physiological and clinical implication.
There are a number of unanswered questions remaining about the
physiological and pathophysiological role of the pressure waveform, some of which are outlined in the introduction. To give definitive answers to these questions, it is essential that we have an apparatus capable of manipulating aortic impedance without affecting other factors. Because we have succeeded in developing such a device, we now
are able to carry out studies to answer some of those questions.
In the physiological setting, the effect of aortic impedance on the
time-varying mechanical properties of both myocardium and cardiac
chambers should be investigated to enable a true understanding of
cardiac mechanics. The effects of aortic impedance on the activation of
the autonomic nerve system and humoral factors might represent an
important area of study. Clinically, by varying impedance and detecting
the initial response that triggers hypertrophy, we may approach the
true mechanical stimulus for myocardial hypertrophy. Various
vasodilators should be reevaluated by identifying any changes in aortic
impedance, and the cardiac effect should be studied by imposing the
same impedance change. Such physiological studies might lead to the
understanding of beneficial effects of vasodilators with no obvious
decrease in pressure.
Limitations.
This system is not capable of regulating mean pressure or resistance.
In addition, this system does not control preload (e.g., end-diastolic
volume) of the left ventricle. Although changes in PP in examples shown
in Fig. 6 are consistent with results from an earlier study (2), the
changes in Ps and Pd values are not necessarily
consistent. This is probably because our system was not capable of
regulating resistance or preload.
To date, applications of this system have been limited to acute
experiments using small, anesthetized animals (whose stroke volume
range was 0.056 ± 0.015 ml). In fact, in rats with larger cardiac
output, the controllable range of impedance tended to be more limited.
A reduction in C of 50% might not be sufficient for some purposes. For
a wider controllable range and experiments using larger animals or
humans, further improvements in pump performance are needed.
Conceivably, however, the application of a device such as an
intra-aortic balloon pump might solve this problem. For the
compensation of servo-system characteristics (transfer function between
servo-command and actual pump volume, low-pass characteristics with a
steep decline of gain >20 Hz; see APPENDIX and Fig.
9), we applied the reciprocal of these
characteristics. This compensation amplified high-frequency noise and
caused some visible oscillations, as shown in Fig. 6, although the
reciprocal filter was truncated at 80-100 Hz. The integration
procedure used to convert flow to volume command partly reduced
high-frequency noise.
View larger version (34K):
[in this window]
[in a new window]
|
Fig. 9.
Characteristics of servo-pump system. A white noise sequence was used
as input to characterize the system (power spectrum at top).
Bode diagrams (gain and phase curves) show frequency responses of
servo-pump system, and coherence function is shown at bottom.
Dotted curves represent closed-loop characteristics of servo-pump as
expressed by the response of the integral of flow waveform at distal
end of tubing to command. Solid curves were obtained after system
bandwidth was effectively widened by modifying the command by the
reciprocal of these characteristics.
|
|
In conclusion, we have developed a servo-pump system that can precisely
control aortic impedance in rats. It imposes a desired impedance on the
in situ left ventricle. This method enables physiological and clinical
studies that may help clarify important aspects of aortic impedance,
such as the load dependence of myocardial mechanical nature and the
true mechanical stimulus required for hypertrophy.
| |
APPENDIX |
Frequency Response of the Servo-Pump System
Open- and closed-loop frequency response of the servo-pump system was
measured with the use of a random command (Gaussian white noise with a
bandwidth of 0.1-1,000 Hz) as the input and the integrated flow
waveform at the distal end of the tubing as the output. Although we
improved the open-loop characteristic by squeezing the distal part of
the tubing to reduce fluid volume and increase resistance, the
bandwidth of the closed-loop system was only 20 Hz with a steep decay
of gain above this frequency (Fig. 9, dotted lines). We effectively
widened the bandwidth by incorporating the reciprocal of this
characteristic into the algorithm. We truncated the reciprocal of this
characteristic for compensation >80 Hz, where pressure and flow power
were insignificant. As shown in Fig. 9 (solid lines), the bandwidth of
the system approached 88 Hz in response to this compensation. The
frequency characteristic of the servo-pump system was updated on-line
during impedance control based on the measured signals, because blood
in the tubing affected the servo-pump characteristics.
| |
ACKNOWLEDGEMENTS |
This study was supported by Research Grants for Cardiovascular
Diseases 6A-4, 7C-2, 7A-1, and 9C-1 from the Ministry of Health and
Welfare of Japan; a Grant from the Science and Technology Agency of
Japan, Encourage System of Center of Excellence; a Grant from the
Ministry of Health and Welfare of Japan, Research on Advanced Medical
Technology; and a Grant from the Ground-Based Research Announcement for
the Space Utilization, promoted by the National Space Development
Agency of Japan and Japan Space Forum.
| |
FOOTNOTES |
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: K. Sunagawa,
Dept. of Cardiovascular Dynamics, National Cardiovascular Center
Research Institute, 5-7-1 Fujishirodai, Suita, Osaka 565-8565, Japan
(E-mail: sunagawa{at}ri.ncvc.go.jp).
Received 27 July 1999; accepted in final form 21 September 1999.
| |
REFERENCES |
1.
Berger, D. S.,
J. K. Li,
and
A. Noordergraaf.
Differential effects of wave reflections and peripheral resistance on aortic blood pressure: a model-based study.
Am. J. Physiol. Heart Circ. Physiol.
266:
H1626-H1642,
1994[Abstract/Free Full Text].
2.
Berger, D. S.,
K. A. Robinson,
and
S. G. Shroff.
Wave propagation in coupled left ventricle-arterial system. Implications for aortic pressure.
Hypertension
27:
1079-1089,
1996[Abstract/Free Full Text].
3.
Brigham, E. O.
The Fast Fourier Transform and its Applications. Englewood Cliffs, NJ: Prentice-Hall, 1988, p. 131-166.
4.
Burkhoff, D.,
J. Alexander, Jr.,
and
J. Schipke.
Assessment of windkessel as a model of aortic input impedance.
Am. J. Physiol. Heart Circ. Physiol.
255:
H742-H753,
1988[Abstract/Free Full Text].
5.
Elzinga, G.,
and
N. Westerhof.
Pressure and flow generated by the left ventricle against different impedances.
Circ. Res.
32:
178-186,
1973[Abstract/Free Full Text].
6.
Gillespie, J. S.,
A. Maclaren,
and
D. Pollock.
A method of stimulating different segments of the autonomic outflow from the spinal column to various organs in the pithed cat and rat.
Br. J. Pharmacol.
40:
257-267,
1970[Web of Science][Medline].
7.
Grossman, W.,
D. Jones,
and
L. P. McLaurin.
Wall stress and patterns of hypertrophy in the human left ventricle.
J. Clin. Invest.
56:
56-64,
1975.
8.
Holt, I. L.,
E. W. Akeyson,
and
M. M. Knuepfer.
Medial medullary contribution to tonic descending inhibition of visceral input.
Am. J. Physiol. Regulatory Integrative Comp. Physiol.
261:
R727-R737,
1991[Abstract/Free Full Text].
9.
Ishide, N.,
Y. Shimizu,
Y. Maruyama,
Y. Koiwa,
T. Nunokawa,
S. Isoyama,
S. Kitaoka,
K. Tamaki,
E. Ino-Oka,
and
T. Takishima.
Effects of changes in the aortic input impedance on systolic pressure-ejected volume relationships in the isolated supported canine left ventricle.
Cardiovasc. Res.
14:
229-243,
1980[Web of Science][Medline].
10.
Kelly, R.,
C. Hayward,
A. Avolio,
and
M. O'Rourke.
Noninvasive determination of age-related changes in the human arterial pulse.
Circulation
80:
1652-1659,
1989[Abstract/Free Full Text].
11.
Kelly, R. P.,
R. Tunin,
and
D. A. Kass.
Effect of reduced aortic compliance on cardiac efficiency and contractile function of in situ canine left ventricle.
Circ. Res.
71:
490-502,
1992[Abstract/Free Full Text].
12.
Kirkpatrick, R. D.,
K. B. Campbell,
D. L. Bell,
and
H. Taheri.
Method for studying arterial wave transmission effects on left ventricular function.
Am. J. Physiol. Heart Circ. Physiol.
260:
H1003-H1012,
1991[Abstract/Free Full Text].
13.
Kobayashi, S.,
M. Yano,
M. Kohno,
M. Obayashi,
Y. Hisamatsu,
T. Ryoke,
T. Ohkusa,
K. Yamakawa,
and
M. Matsuzaki.
Influence of aortic impedance on the development of pressure-overload left ventricular hypertrophy in rats.
Circulation
94:
3362-3368,
1996[Abstract/Free Full Text].
14.
Konstam, M. A.,
M. F. Rousseau,
M. W. Kronenberg,
J. E. Udelson,
J. Melin,
D. Stewart,
N. Dolan,
T. R. Edens,
S. Ahn,
D. Kinan,
D. M. Howe,
L. Kilcoyne,
J. Metherall,
C. Benedict,
S. Yusuf,
and
H. Pouleur.
Effects of the angiotensin converting enzyme inhibitor enalapril on the long-term progression of left ventricular dysfunction in patients with heart failure. SOLVD Investigators.
Circulation
86:
431-438,
1992[Abstract/Free Full Text].
15.
Latson, T. W.,
W. C. Hunter,
N. Katoh,
and
K. Sagawa.
Effect of nitroglycerin on aortic impedance, diameter, and pulse-wave velocity.
Circ. Res.
62:
884-890,
1988[Abstract/Free Full Text].
16.
Maruyama, Y.,
O. Nishioka,
E. Nozaki,
H. Kinoshita,
H. Kyono,
Y. Koiwa,
and
T. Takishima.
Effects of arterial distensibility on left ventricular ejection in the depressed contractile state.
Cardiovasc. Res.
27:
182-187,
1993[Abstract/Free Full Text].
17.
Mitchell, G. F.,
M. A. Pfeffer,
P. V. Finn,
and
J. M. Pfeffer.
Equipotent antihypertensive agents variously affect pulsatile hemodynamics and regression of cardiac hypertrophy in spontaneously hypertensive rats.
Circulation
94:
2923-2929,
1996[Abstract/Free Full Text].
18.
Miyashita, H.,
U. Ikeda,
Y. Tsuruya,
H. Sekiguchi,
K. Shimada,
and
T. Yaginuma.
Noninvasive evaluation of the influence of aortic wave reflection on left ventricular ejection during auxotonic contraction.
Heart Vessels
9:
30-39,
1994[Web of Science][Medline].
19.
Murgo, J. P.,
N. Westerhof,
J. P. Giolma,
and
S. A. Altobelli.
Aortic input impedance in normal man: relationship to pressure wave forms.
Circulation
62:
105-116,
1980[Free Full Text].
20.
Nichols, W. W.,
and
M. F. O'Rourke.
McDonald's Blood Flow in Arteries (3rd ed.). London: Arnold, 1990, p. 398-415.
21.
Oppenheim, A. V.,
and
R. W. Schafer.
Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975, p. 337-375.
22.
Randall, O. S.,
G. C. van den Bos,
and
N. Westerhof.
Systemic compliance: does it play a role in the genesis of essential hypertension?
Cardiovasc. Res.
18:
455-462,
1984[Web of Science][Medline].
23.
Suga, H.,
A. Kitabatake,
and
K. Sagawa.
End-systolic pressure determines stroke volume from fixed end-diastolic volume in the isolated canine left ventricle under a constant contractile state.
Circ. Res.
44:
238-249,
1979[Free Full Text].
24.
Sunagawa, K.,
D. Burkhoff,
K. O. Lim,
and
K. Sagawa.
Impedance loading servo pump system for excised canine ventricle.
Am. J. Physiol. Heart Circ. Physiol.
243:
H346-H350,
1982.
25.
Westerhof, N.,
G. Elzinga,
and
P. Sipkema.
An artificial arterial system for pumping hearts.
J. Appl. Physiol.
31:
776-781,
1971[Free Full Text].
26.
Westerhof, N.,
and
M. F. O'Rourke.
Haemodynamic basis for the development of left ventricular failure in systolic hypertension and for its logical therapy.
J. Hypertens.
13:
943-952,
1995[Web of Science][Medline].
27.
Yaginuma, T.,
A. Avolio,
M. O'Rourke,
W. Nichols,
J. J. Morgan,
P. Roy,
D. Baron,
J. Branson,
and
M. Feneley.
Effect of glyceryl trinitrate on peripheral arteries alters left ventricular hydraulic load in man.
Cardiovasc. Res.
20:
153-160,
1986[Web of Science][Medline].
Am J Physiol Heart Circ Physiol 278(3):H998-H1007
0363-6135/00 $5.00
Copyright © 2000 the American Physiological Society
TOP
ABSTRACT
INTRODUCTION
