Continuous stroke volume monitoring by m (1)

Clinical Science (1999) 97, 291–301 (Printed in Great Britain)

Continuous stroke volume monitoring by
modelling flow from non-invasive
measurement of arterial pressure
in humans under orthostatic stress
Mark P. M. HARMS*, Karel H. WESSELING†, Frank POTT‡, Morten JENSTRUP‡,
Jeroen VAN GOUDOEVER†, Niels H. SECHER‡, and Johannes J. VAN LIESHOUT*
*Department of Internal Medicine, Academic Medical Center, Cardiovascular Research Institute, Amsterdam, The Netherlands,
†Netherlands Organization for Applied Scientific Research, TNO Biomedical Instrumentation, Amsterdam, The Netherlands, and
‡Department of Anesthesia, Rigshospitalet, The Copenhagen Muscle Research Center, Copenhagen, Denmark

A

B

S

T

R

A

C

T

The relationship between aortic flow and pressure is described by a three-element model of the
arterial input impedance, including continuous correction for variations in the diameter and the
compliance of the aorta (Modelflow). We computed the aortic flow from arterial pressure by this
model, and evaluated whether, under orthostatic stress, flow may be derived from both an
invasive and a non-invasive determination of arterial pressure. In 10 young adults, Modelflow
stroke volume (MFSV) was computed from both intra-brachial arterial pressure (IAP) and noninvasive finger pressure (FINAP) measurements. For comparison, a computer-controlled series
of four thermodilution estimates (thermodilution-determined stroke volume ; TDSV) were
averaged for the following positions : supine, standing, head-down tilt at 20 ° (HDT20) and headup tilt at 30 ° and 70 ° (HUT30 and HUT70 respectively). Data from one subject were discarded
due to malfunctioning thermodilution injections. A total of 155 recordings from 160 series were
available for comparison. The supine TDSV of 113³13 ml (mean³S.D.) dropped by 40 % to
68³14 ml during standing, by 24 % to 86³12 ml during HUT30, and by 51 % to 55³15 ml during
HUT70. During HDT20, TDSV was 114³13 ml. MFSV for IAP underestimated TDSV during
HDT20 (®6³6 ml ; P ! 0.05), but that for FINAP did not (®4³7 ml ; not significant). For

HUT70 and standing, MFSV for IAP overestimated TDSV by 11³10 ml (HUT70 ; P ! 0.01) and
12³9 ml (standing ; P ! 0.01). However, the offset of MFSV for FINAP was not significant for
either HUT70 (3³8 ml) or standing (3³9 ml). In conclusion, due to orthostasis, changes in the
aortic transmural pressure may lead to an offset in MFSV from IAP. However, Modelflow
correctly calculated aortic flow from non-invasively determined finger pressure during
orthostasis.

INTRODUCTION
In order to evaluate the mechanisms leading to syncope,
a continuous recording of blood pressure and ideally also

stroke volume is required, because events proceed rapidly
[1–3]. Invasive procedures themselves can induce a
neurally mediated syncope, and therefore blood pressure
should preferably be recorded non-invasively [4,5]. The

Key words : cardiovascular, fingers, posture, thermodilution, tilt-table test.
Abbreviations : FINAP, finger arterial pressure ; HDT20, head-down tilt at 20 ° ; HUT30 and HUT70, head-up tilt at 30 ° and 70 °
respectively ; IAP, intra-brachial arterial pressure ; MFSV, Modelflow stroke volume ; TDSV, thermodilution-determined stroke
volume.

Correspondence : Dr J. J. van Lieshout, Department of Internal Medicine, Room F4–264, Academic Medical Center, University of
Amsterdam, P.O. Box 22700, 1100 DE Amsterdam, The Netherlands.

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least intrusive technique available that adequately
monitors changes in arterial pressure is the finger volume
clamp method [5].
Application of pulse wave analysis to the measurement
of finger arterial pressure (FINAP) offers a non-invasive
and continuous recording of stroke volume. The analysis
is based on models of the arterial system that assume that
both the aortic dimension and the elastic properties
remain constant [6,7], although these are known to

change when the distending pressure of the aorta is
changed [8]. A three-element model of the arterial input
impedance (Modelflow) has been advanced that takes
into account the non-linear aortic pressure–area relationship [9]. Modelflow computes a flow wave from the
arterial pressure wave that is integrated to obtain the
stroke volume of the heart.
Head-up tilt testing is used for the evaluation of
patients with neurally mediated syncope [5,10]. A change
in body position influences the effect of gravity on the
cardiovascular system, thereby changing the sympathetic
tone to the heart and blood vessels [11]. In response to the
assumption of an upright position, either actively by
standing up or passively by head-up tilt, sympathetic
outflow increases [12], whereas in the head-down position sympathetic tone decreases [13]. Also, the upright
position raises the hydrostatic pressure in the arteries
below the hydrostatic indifference point, which is located
approximately at the level of the left ventricle, and
therefore reduces the pressure in arteries above that level
[11,14]. Both head-up and head-down tilt may change the
arterial input impedance by modulating sympathetic tone

and transmural vascular pressures. The Modelflow computation of stroke volume is, however, based on a supine
model of the arterial haemodynamic characteristics, and
it is unclear whether, under conditions of orthostatic
stress, stroke volume can be derived from the arterial
pressure wave. Therefore we addressed whether the
Modelflow approach, validated for supine intra-arterial
pressure [15], is also applicable during orthostatic stress.
The study, using awake healthy subjects under varying
degrees of active or passive orthostatic stress, was
designed to compare the thermodilution-determined
stroke volume (TDSV) with the Modelflow stroke
volume (MFSV) obtained from intra-brachial arterial
pressure (IAP) and from non-invasively determined
FINAP.

METHODS
Subjects
Ten healthy subjects (nine males) were studied ; each gave
informed consent, and the study was approved by the
Ethical Committee of Copenhagen. The mean age was 29

years (range 20–39 years), with a mean height of 183 cm
(range 170–191 cm) and a mean weight of 74 kg (range
# 1999 The Biochemical Society and the Medical Research Society

Table 1 Subject details and the calibration factor, K, for
MFSV IAP and MFSV FINAP

In subject S8, the difference between mean K values for IAP and FINAP was related
to cuff malpositioning on the finger.

K
Subject

Age
Height
Gender (years) (cm)

Weight
(kg)

MFSVIAP

MFSVFINAP

S1
S2
S3
S4
S5
S6
S7
S8
S9
S10

M
M
F
M
M

M
M
M
M
M

78
80
71
78
68
68
74
82
70
72

1.33
0.95
1.32

1.25
–
1.16
1.19
1.14
1.16
1.34

1.02
0.85
1.13
0.98
–
1.09
1.17
1.99
1.24
1.19

Mean³S.D.

32
34
39
30
20
34
26
25
22
23

183
191
170
181
178
179
188
190

182
187

29³6 183³6 74³5

1.20³0.12 1.18³0.32

68–82 kg) (Table 1). All subjects had normal physical
fitness without sports training. They had no history of
orthostatic fainting and used no medication.

Pressure measurements
Under local anaesthesia (2 % lidocaine), a catheter (20 G ;
internal diam. 1.0 mm) was placed in the brachial artery
(radial artery in subject S2) of the non-dominant arm, and
a balloon-tipped thermodilution catheter (model 93A831H-7.5F ; Baxter Healthcare Corp., Irvine, CA, U.S.A.)
was introduced percutaneously through the left basilic
vein under continuous ECG recording. Correct catheter
positioning was confirmed by monitoring the pressure
waveform. IAP, pulmonary artery pressure and right
atrial pressure were measured using Baxter disposable
transducers. To minimize hydrostatic errors during
changes in body position, the transducers were fixed to
the left upper arm at the level of the right atrium.
Catheter lumens were flushed continuously.
A good-quality intra-arterial pressure signal is a
prerequisite for correct computation of the MFSV. The
tubing of the catheter}manometer system has to be noncompliant and the catheter system must be free of clots
and air bubbles. Sufficient signal quality should be
assessed by checking the dynamic performance of the
arterial pressure measurement system. Maintenance of an
adequate resonance frequency (range 12–25 Hz) [16] was
confirmed before and after completion of the protocol.
FINAP was measured non-invasively with a Finapres
model 5 [Netherlands Organization for Applied Scientific Research, Biomedical Instrumentation (BMITNO)]. The Finapres is based on the volume-clamp
technique of Pen4 a! z [17] and the Physiocal criteria of

Stroke volume from non-invasive blood pressure

Figure 1

Diagram of modelling flow from measurements of arterial pressure

Left panel : non-invasive FINAP as input to the model for one heartbeat. Middle panel : three-element model of the aortic input impedance used to compute flow from
pressure. Z 0, characteristic impedance of the proximal aorta ; C w, ‘ Windkessel ’ compliance of the arterial system ; R p, total systemic peripheral resistance. The Z 0 and
C w elements have non-linear, pressure-dependent properties indicated by the stylized ! symbol. The peripheral resistance element, R p, varies with time, as symbolized
by the arrow. P (t), arterial pressure waveform ; Q (t), blood flow as a function of time ; Pw (t) Windkessel pressure. Right panel : the computed output of the model,
i.e. aortic flow as function of time.
Wesseling et al. [18]. In order to avoid hydrostatic level
errors, the cuff was applied to the mid-phalanx of the
third finger of the hand contra-lateral to the cannulated
arm and held at level of the right atrium in the midaxillary line. The positions of the finger cuff and pressure
transducer were checked for possible hydrostatic level
errors and occasionally re-adjusted. In the Finapres
device, the Physiocal expert system was in operation to
establish and maintain a correct volume-clamp set-point
[18]. Mean arterial pressure (FINAP and IAP) was
obtained as the integral of pressure over each beat divided
by the corresponding beat interval.

Thermodilution
The thermodilution catheter was connected to a Baxter
COM-2 cardiac output computer (Baxter-Edwards). A
10 ml sample of iced glucose solution (5 %) was
drawn from a CO-SET cooling unit (Baxter) and injected
by a pneumatic power injector (Broszeit Medizintechnik)
over C 3 s [19]. Following the passage of the thermodilution curve and after at least 18 s, the syringe was
refilled automatically. Each thermodilution curve was
checked visually for shape and appearance time before
acceptance. One thermodilution cardiac output estimate
was taken as the average obtained from four random
injections. In all subjects (except S10), each series of four
thermodilution injections was preceded by one manual
injection in order to prime the syringe and the catheter
with cold liquid.

Calculation of MFSV
Beat-to-beat stroke volume was estimated by the
Modelflow method (Figure 1). The method uses a nonlinear, three-element model of the aortic input impedance
to compute an aortic flow waveform from the arterial

pressure wave. The flow waveform is integrated per beat
to yield stroke volume (see Appendix).

Experimental protocol
After an overnight fast, the subjects were attached to
instruments at 09.00 hours in a room with an ambient
temperature of 22 °C, and a test run was performed to
familiarize the subject with the protocol. The protocol
started with a period of supine rest, after which periods of
standing and tilting at various angles were interspaced
with further periods of supine rest to re-establish baseline
levels (Figure 2). In each position, one or more series of
four thermodilution cardiac output estimates were performed. All subjects were observed by the same physician. The prolonged orthostatic stress was terminated by
returning the subject to the horizontal position after
either 60 min of head-up tilt or 10 min in the active
standing position (or earlier at the subject’s request), or
when blood pressure had decreased by " 20 mmHg
(systolic) or " 5 mmHg (diastolic) [20]. Consequently,
the full protocol could not always be completed.

Data acquisition and analysis
A PC-based system was used to control and mark the
thermodilution injections, to start the COM-2, and to
read its output via the serial port. An event marker was
used to identify the onset of changes in posture. IAP,
pulmonary arterial pressure, right atrial pressure, FINAP
and marker signals were sampled at 100 Hz, stored on
disk and also recorded on a polygraph (Graphtec) for online inspection. Signals to and from the computer were
routed through an interface providing electrical isolation.
Signals requiring offset and sensitivity adjustments went
through additional variable offset and gain amplifiers.
For the determination of cardiac output by averaging
series of four thermodilution estimates, haemodynamic
variables must remain relatively stable [21,22]. The
stability of the signals was verified by examining heart
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Figure 2

Experimental protocol

Thermodilution estimates were taken 10 min after the start of each supine rest period, after 5 and 10 min of active standing, after 5 min of HDT5, HDT10, HDT20
and HUT30 positions, and every 10 min during sustained HUT70. A maximum of six cardiac output estimates were obtained during 1 h of HUT70. Arrows indicates the
times of the thermodilution measurements.

Figure 3 Stable (left panels) and unstable (right panels) haemodynamic states in a series of four thermodilution (TD)
estimates

(A) Intra-arterial pressure (IAP), pulmonary artery pressure (PAP) and right atrial pressure (RAP). Rectangles indicate the duration of one TD series. (B) Detail of (A),
showing the plotted signals of systolic (SAP), mean (MAP), diastolic (DAP) and mean pulmonary (MPAP) arterial pressures, mean right atrial pressure (MRAP), and heart
rate (HR) during TD1–TD4. One TD measurement takes 18 s. Note the difference in the variability of the signals between a stable and an unstable haemodynamic state.
rate, systolic, mean and diastolic arterial pressures, and
mean pulmonary arterial and mean right atrial pressures
over the episodes of each individual thermodilution
estimate (Figure 3). If any variable differed by more than
10 % from the mean of the series, the series was rejected
# 1999 The Biochemical Society and the Medical Research Society

[23]. To obtain unbiased averages of the thermodilutiondetermined cardiac output, injections must be executed at
random phases of the respiratory cycle. In this study,
injections were at regular intervals of 36 s and, since
respiration was spontaneous and irregular, the injection

Stroke volume from non-invasive blood pressure

moment was assumed to be ‘ random ’. This was tested for
each subject by two-way analysis of variance.
Stroke volume was calculated from the IAP and the
FINAP waves, giving two estimates of arterial-pressurederived stroke volume : MFSVIAP and MFSVFINAP. The
average of a series of four thermodilution cardiac output
estimates was divided by the heart rate over the corresponding period to obtain the average TDSV. Thus
three simultaneous estimates of stroke volume were
available for analysis for each series. The supine average
TDSV was used to calibrate the pressure-derived stroke
volumes by multiplying the uncalibrated model stroke
volume by the ratio (calibration factor K) of TDSV to
either MFSVIAP or MFSVFINAP.
The pooled data and stroke volumes during HUT70
(head-up tilt at 70°) were not normally distributed, and
are expressed as means with ranges. The data obtained for
the HDT20 (head-down tilt at 20°), HUT30 (head-up tilt
at 30°) and standing positions were normally distributed,
and are expressed as means³S.D. For the supine position,
six or seven values were available ; in the standing position
two to four values ; and in the HUT70 position one to
seven values. One value was available for each of the
HUT30 and HDT20 positions. TDSV was compared
with MFSVIAP and MFSVFINAP for all body positions by
linear regression. The distribution of changes with body
position was examined by repeated-measures analysis of
variance on ranks. Significant differences were identified
by subsequent multiple-comparison testing (Student–
Neuman–Keuls). Differences between MFSVIAP and
MFSVFINAP, and deviations from TDSV, were evaluated
with parametric or non-parametric tests. A P value of
! 0.05 was considered to indicate a statistically significant difference.

RESULTS
In subject S5, thermodilution injections required as much
as 10 s rather than the usual 3 s, and errors and alerts were

Table 3 Group-average values for correlation coefficient r
and offset for MFSV from IAP and FINAP values

Data were obtained for the various body positions. ‘ All ’ gives pooled data from
all manoeuvres. Significance of correlations : *P ! 0.01 ; **P! 0.001.
Significance of offset from TDSV values : †P ! 0.05 ; ††P ! 0.01.
MFSVFINAP

All
HDT20
Standing
HUT30
HUT70

MFSVIAP

Offset

r

Offset

r

1 (®16 to 33)
®4³7
3³9
5³2
3 (®6 to 33)

0.97**
0.87*
0.78**
0.98**
0.87**

4 (®16 to 51)††
®6³6†
12³9††
6³3
11 (®1 to 51)††

0.94**
0.90**
0.84**
0.99**
0.83**

frequently noted. An analysis of variance showed systematic differences in stroke volume within a series of
four injections, but not between the manoeuvres, while in
all other subjects the significant variation was between
manoeuvres and not within the series of four injections ;
therefore this subject was excluded from the analysis. In
two subjects, active standing had to be terminated after 4
and 5 min respectively because they experienced presyncopal symptoms with a fall in blood pressure. In four
subjects, HUT70 was terminated after 9, 9.5, 28 and
34 min respectively because of near-fainting ; three of the
subjects had a fall in blood pressure, and one subject was
tilted back on his own request.
A total of 160 TDSV series were therefore available
from the nine remaining subjects. The 10 % criterium for
haemodynamic stability was not fulfilled in two series
(two subjects). Due to an unnoticed displacement of the
finger cuff, three series in subject S8 in the HUT70
position were rejected. Thus 155 series (97 %) of
MFSVIAP and MFSVFINAP values remained available for
comparison. For both pressure sites, the calibration value
(K) is listed in Table 1. In six of the nine subjects the
finger cuff was repositioned to another finger of the same

Table 2 TDSV, mean IAP, mean FINAP, heart rate (HR), mean pulmonary artery pressure (PAP)
and mean right atrial pressure (RAP) in each subject

Values are ranges.
Subject

TDSV (ml)

IAP (mmHg)

FINAP (mmHg)

HR (beats/min)

PAP (mmHg)

RAP (mmHg)

S1
S2
S3
S4
S6
S7
S8
S9
S10

45–120
33–105
45–102
41–128
51–112
63–136
54–137
73–121
44–121

84–110
86–96
93–113
86–97
68–83
82–89
78–105
82–95
85–104

88–117
73–90
84–111
94–112
69–99
73–91
69–107
113–137
96–127

62–116
46–86
52–114
62–108
54–81
48–88
48–87
44–82
44–72

7–21
6–18
5–16
10–18
4–18
10–18
10–16
9–19
3–12

0–8
0–5
0–6
1–5
®1 to 3
3–6
®1 to 4
0–6
0–6

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Figure 4

Pooled data for the two pressure sites

Left panels : regression of pooled data for TDSV against MFSV. Right panels : scatter diagrams of the differences between TDSV and MFSV against their means. Horizontal
lines indicate mean³1.96 S.D.

Figure 5

Stroke volumes for different body positions

Key : TD, TDSV ; MFfin, MFSVFINAP ; MFiap, MFSVIAP.
hand because of discomfort in the cuffed finger, usually
after 2 h of continuous monitoring. After repositioning
of the cuff to another finger, the study was continued,
usually within 5 min, when a reliable stable FINAP was
confirmed by checking waveform and blood pressure
level. Repositioning of the cuff did not affect the FINAP
or calculated stroke volume. Differences between TDSV
and MFSVIAP or MFSVFINAP were not dependent on
blood pressure or heart rate.
# 1999 The Biochemical Society and the Medical Research Society

Stroke volume
TDSV ranged from 33 to 137 ml (Table 2). The difference
between TDSV and MFSVFINAP [range ®16 to 33 ml ;
not significant] was smaller than that between TDSV and
MFSVIAP (range ®16 to 51 ml ; P ! 0.01) (Table 3 ;
Figure 4).

Supine position and head-down tilt
TDSV did not change significantly from the supine to the

Stroke volume from non-invasive blood pressure

Table 4

Individual changes in FINAP and IAP during HUT70

In subject S8, the finger cuff was switched to another position during tilt-up ; bs,
before switch ; as, after switch.
Subject

Tilt duration
(min)

∆IAP
(mmHg)

∆FINAP
(mmHg)

∆(IAP–FINAP)
(mmHg)

S1
S2
S3
S4
S6
S7
S8 bs
S8 as
S9
S10

30
22
50
50
8
49
14
23
30
8

14.7
®12.9
8.8
9.3
1.7
11.2
®1.2
1.9
®1.5
®13.2

20.4
®9.1
16.3
4.2
10.2
9.4
8.1
9.0
®1.7
®5.4

®5.7
®3.8
®7.5
5.1
®8.5
1.8
®9.3
®7.1
0.2
®7.8

Mean³S.D.

28.4³16.6

1.9³9.6

6.1³9.3

®4.3³5.0

head-down tilt position [values of 113³12 ml (range
81–137 ml) and 114³13 ml (range 94–133 ml) respectively]. Both indices of MFSV tended to underestimate
TDSV during HDT20, but the offset was significant only
for MFSVIAP (®6³6 ml, compared with ®4³7 ml for
MFSVFINAP) (Table 3 ; Figure 5).

Head-up tilt and standing
On moving from the supine position to the HUT30
position, TDSV decreased by 24 %, to 86³12 ml (range
60–103 ml) (Figure 5). In the upright body position,
MFSV overestimated TDSV. The difference compared
with TDSV was similar for MFSVFINAP (5³2 ml) and
MFSVIAP (6³3 ml ; not significant) (Table 3). In the
HUT70 position, TDSV dropped by 51 % to 55 ml
(range 33–83 ml) ; the offset of MFSVFINAP from TDSV
was not significant [3 ml (®6 to 33 ml)], unlike that of
MFSVIAP from TDSV [11 ml (®1 to 51 ml ; P ! 0.01)].
During head-up tilt, there was no systematic trend in the
differences between FINAP and IAP (Table 4). On
moving from the supine position to standing, TDSV
decreased by 40 % to 68 ml (range 41–94 ml) (Figure 5).
For MFSVFINAP the offset induced by standing (3³9 ml)
was not significant, unlike that for MFSVIAP (12³9 ml ;
P ! 0.01) (Table 3).

Tracking of stroke volume
In all subjects except one, MFSVFINAP tracked TDSV in
all body positions, including HUT70 for 1 h (Figure 6).
In subject S10, MFSVFINAP deviated from TDSV during
orthostatic stress, giving an underestimate of the orthostatic fall in TDSV.

Figure 6

TDSV and MFSV FINAP values in the individual subjects

Solid line, TDSV ; broken line, MFSVFINAP. Changes in stroke volume are shown as
elicited by active standing and by passive changes in body position between HDT20
and HUT70.

DISCUSSION
The present study investigated whether the decrease in
cardiac stroke volume evoked by orthostatic stress can be
derived from a non-invasive arterial pressure waveform
using a model based on haemodynamic characteristics of
the human aorta in the supine position. In young adults
it was demonstrated that stroke volume as obtained by
simulation of this model using a non-invasively determined arterial pressure reflects the TSDV, with a nonsignificant offset over the full range of stroke volume
changes observed during postural changes.

Body position and MFSV
Under varying degrees of active and passive orthostatic
stress in humans, an accepted method for computing
stroke volume from arterial pressure is not available. We
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compared a beat-by-beat determination of stroke volume
with a determination based on thermodilution, i.e. a
discontinuous method integrating over several heart
beats. The Modelflow method uses a three-element model
of the aortic input impedance to compute flow from the
pulsation of the arterial pressure [15]. The mechanical
properties of the aorta dominate the impedance to
outflow that is presented to the left ventricle in systole,
which depends in turn on the difference between the
intra-arterial pressure and the tissue pressure exerted on
the outside of the aortic and arterial wall, i.e. the
transmural pressure.
On moving from the supine to the upright position,
the intra-arterial pressure below the level of the heart
increases in proportion to the hydrostatic height, but it is
not known to what extent this rise in pressure is
counterbalanced by an increased tissue pressure, and the
respiratory movement-related abdomino–thoracic pump
may also be of importance. Therefore it is unclear
whether the orthostatic increment in intravascular
pressures is translated into an increase in transmural
pressure in the descending thoracic and abdominal aorta
[11,14,24,25].
Assumption of the upright position, either as a
voluntary effort during standing or as a passive movement during head-up tilt, might increase the aortic
transmural pressure below the level of the heart, and
consequently reduce its compliance. A reduction in
compliance of the aorta implies that, for a given pressure,
the actual volume of blood stored in the aorta becomes
less than the volume computed from the three-element
model of aortic input impedance [15], which mimics the
impedance of the aorta in the supine position. This view
is supported by the finding that, in comparison with the
TDSV estimate, the computed MFSV was greater in the
upright body position and smaller in the head-down
position, but only when the MFSV was based on an intraarterial reading of blood pressure.
The cardiovascular stress is intensified during maintained head-up tilt, with amplification of reflex vasoconstriction [26]. Maintaining the HUT70 position for
1 h, however, did not influence the offset of the MFSV,
and we take this to imply that the estimate of peripheral
vascular resistance included in the model [15] is simulated
appropriately.

Accuracy of thermodilution method
We attributed the differences between MFSV [15] and
TDSV estimates entirely to the model. The thermodilution method is based on the law of conservation of
energy, i.e. that the temperature at the site of injection
is the same as that at the site of detection, that mixing
of the indicator and blood is complete, that the induced
temperature change can be discriminated accurately from
the fluctuations in baseline temperature, and that blood
flow remains constant while the measurement is made
# 1999 The Biochemical Society and the Medical Research Society

[22]. In the present study, the temperature of the indicator
was measured at the entrance of the catheter lumen and
corrected for. Iced injection fluid yields a greater signalto-noise ratio of the thermodilution signal and a lower
variance of consecutive measurements than an equivalent
volume of injection fluid at room temperature [22]. The
addition of heat to the syringe by direct hand contact [27]
was avoided by using an automatic injector in combination with a closed delivery system that also reduced
injection time and improved consistency in injected
volume and linearity of injection rate [28]. The Stewart–
Hamilton equation used to calculate the area under the
thermodilution curve is valid for constant blood flow
only [21,22]. Prolonged orthostatic stress elicits central
hypovolaemia by continued pooling of fluid in the legs
and splanchnic venous beds, and amplification of reflex
vasoconstriction [29,30]. This introduces oscillations in
the central and arterial pressures, as well as in cardiac
output ; these are amplified further by respiration (Figure
3), which inevitably increases the scatter of thermodilution estimates.
We restricted the influence of the respiratory
oscillations on cardiac output in two ways. First, by
distributing four injections randomly throughout the
respiratory cycle, the accuracy of the series-average
cardiac output improves with the square root of the
number of observations [19]. Secondly, we excluded
from the analysis the cardiac output series obtained
under conditions when pressures and heart rate deviated
by more than 10 % from their average values (Figure 3).
Nevertheless, in awake subjects the prerequisite of
constancy of blood flow during the period of the dilution
curve may not be fully established during orthostasis,
with an ongoing accumulation of blood in the legs and
the occurrence of cardiovascular reflex responses to it.
Absolute values for stroke volume are preferred, and
model calibration against a standard is recommended, for
both non-invasive and invasive arterial pressure measurements. On the other hand, for purposes of orthostatic
stress testing and in ambulant patients, a continuous
measure of stroke volume is preferably non-invasive, and
absolute values of stroke volume are less relevant [4,5].

Site of pressure measurement
In the head-down position, the offset of the MFSV
obtained from both pressure sites was small. After
transition to the upright position, the increase in the
offset was significant only for MFSV based on IAP, and
not for that based on FINAP. A change in arterial
pressure due to a hydrostatic level error of the pressure
transducer introduced by the change in body position is
a possibility, although we attempted to minimize changes
in the height of the arterial pressure transducer with
respect to the level of the heart. In addition, an
orthostasis-related downward shift of the heart might

Stroke volume from non-invasive blood pressure

have introduced a hydrostatic error in the measurement
of arterial pressure. Since no systematic trend was found
in the difference between FINAP and IAP (Table 4), we
consider that the contribution of possible hydrostatic
level errors in arterial pressure to the offset of MFSV to
be small.
Changes in the aortic transmural pressure due to
orthostasis may lead to an offset in stroke volume derived
from IAP that is not accounted for by the model. During
postural changes, an offset in MFSV as obtained from
IAP, but not from FINAP, is remarkable. In the upright
position, FINAP readings differ from those of IAP [31].
Apparently the hypothesized changes in arterial compliance due to orthostasis not accounted for by the model
were compensated for by the level of arterial pressure
measured in the finger.

ACKNOWLEDGMENTS
This study was supported by the Danish National
Research Foundation (grant no. 504-14) and the
Netherlands Heart Foundation (grant no. 94.132). We
thank Heidi Hansen, Anne Katherine Secher and Annette
Uhlmann for technical assistance.

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N. T. (1983) A simple device for the continuous
measurement of cardiac output. Adv. Cardiovasc. Phys. 5II, 16–52
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M. P. M. Harms and others

APPENDIX
Calculation of stroke volume
The Modelflow method computes an aortic flow waveform from a peripheral arterial pressure signal. It uses a
non-linear three-element model of the aortic input
impedance. The haemodynamic behaviour of the aorta in
opposing ejection of blood from the left ventricle has
been described by a three-element model of the arterial
input impedance [1–3]. The three elements correspond to
the characteristic impedance of the aorta (the opposition
to the pulsatile flow from the left ventricle), the total
arterial compliance (opposition to an increase in aortic
blood volume), and a peripheral vascular resistance.
The first element in the model is the aortic characteristic impedance (Z ) ; this describes the relationship
!
between pulsatile flow and pressure at the entrance to the
aorta. The rise in pressure will depend on the instantaneous flow, on the cross-sectional area of the aorta and
on the aortic compliance. Hence Z represents the aortic
!
opposition to pulsatile inflow from the contracting left
ventricle. Z has the dimension of pressure divided by
!
flow. The second model element is the arterial compliance
(Cw) ; this describes how much the aortic pressure rises
for a given volume of blood, and represents the aortic
opposition to an increase in blood volume. Compliance is
defined as a change in volume (dV) divided by a change in
pressure (dP). The third element in the model is peripheral vascular resistance (Rp). Rp is a measure of the
ease of constant blood drainage from the Windkessel into
the peripheral vascular beds. Rp is defined as the ratio of
mean pressure to mean flow, and is not a major
determinant of systolic inflow [4].
The first two elements of the model, Z and Cw, are
!
thus dependent on the elastic properties of the aorta. In
earlier models of the arterial system, changes in aortic
volume were assumed to be linearly related to the aortic
pressure [1–3]. From Langewouters’ studies on the elastic
properties of human thoracic and abdominal aortas, it
was found that the aortic properties vary in a non-linear
manner with distending pressure. The change in thoracic
aortic cross-sectional areas was described as an arctangent
function of transmural pressure [5]. The model uses this
property and is non-linear, thus mimicking the haemodynamic behaviour of the aorta in detail (see Figure 1). It
computes two of the model parameters, Z and Cw,
!
making use of a built-in database of arctangent area–
pressure relationships, given subject gender and age as
input [5]. Instantaneous values of Cw and Z are used in
!
the model simulation, resulting in the computation of an
aortic flow waveform. Rp, the third element, is calculated
for each beat by the model simulation and updated.
Thus the Modelflow method computes stroke volume
from the arterial pressure wave, with continuous nonlinear corrections for variations in aortic diameter,
compliance and impedance during the arterial pulsation
# 1999 The Biochemical Society and the Medical Research Society

[4]. Integrating the aortic flow waveform per beat
provides left-ventricular stroke volume. Cardiac output
is computed by multiplying stroke volume by heart rate.
Only if absolute values for stroke volume are required
does MFSV need calibration against a ‘ golden ’ standard,
e.g. thermodilution. Otherwise stroke volume can be
expressed as changes from control with the same precision in stroke volume tracking.
Aortic pressure, theoretically preferred in the model, is
not routinely available in clinical practice, and therefore a
peripheral arterial pressure is used. Peripherally measured
arterial pressure is, however, distorted in comparison
with aortic pressure. Although the calculated flow
waveform is therefore distorted also, the area under the
flow wave, which equals the stroke volume, was shown
to be affected only minimally by such distortion [4]. The
effect is that peripheral arterial pressures, including noninvasive FINAP, appear sufficiently close to the aortic
pressure to be applied in the model and still allow reliable
estimations of stroke volume [4,6]. Correct tracking of
IAP by non-invasive FINAP is a prerequisite for such a
correct computation of model-simulated stroke volume,
as demonstrated in healthy subjects [7–9] and in patients
with co-existing hypertension and vascular disease [10].
The cross-sectional area of the aorta is increased in
arteriosclerotic aortas, along with increased stiffness. The
net effect of both increments is that they compensate for
each other in their effects on compliance, such that the
compliant behaviour of an arteriosclerotic aorta is almost
identical with that of a non-sclerotic aorta over the
physiological pressure range [11]. Studies in patients with
cardiovascular disease demonstrated that Modelflow
values from arterial pressure accurately track changes in
cardiac output in both direction and degree when
compared with thermodilution-based estimates [4,6,12].

REFERENCES
1 Broemser, P. and Ranke, O. F. (1930) Uber die Messung
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Biol. (Munich) 90, 467–507
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compliance during pressure transients. Am. J. Physiol. 252,
H1275–H1283
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Assessment of Windkessel as a model of aortic input
impedance. Am. J. Physiol. 255, H742–H753
4 Wesseling, K. H., Jansen, J. R. C., Settels, J. J. and
Schreuder, J. J. (1993) Computation of aortic flow from
pressure in humans using a nonlinear, three-element
model. J. Appl. Physiol. 74, 2566–2573
5 Langewouters, G. J., Wesseling, K. H. and Goedhard, W. J.
A. (1984) The static elastic properties of 45 human thoracic
and 20 abdominal aortas in vitro and the parameters of a
new model. J. Biomech. 17, 425–535
6 Jellema, W. T., Wesseling, K. H., Groeneveld, A. B. J.,
Stoutenbeek, C. P., Thijs, L. G. and Van Lieshout, J. J.
(1999) Continuous cardiac output in septic shock by
simulating a model of the aortic input impedance. A

Stroke volume from non-invasive blood pressure

comparison with bolus injection thermodilution.
Anesthesiology 90, 1317–1328
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N. H. (1990) Non-invasive blood pressure monitoring
during head-up tilt using the Penaz principle. Acta
Anaesthesiol. Scand. 34, 519–522
8 Petersen, M. E., Williams, T. R. and Sutton, R. (1995) A
comparison of non-invasive continuous finger blood
pressure measurement (Finapres) with intra-arterial
pressure during prolonged head-up tilt. Eur. Heart J. 16,
1641–1654
9 Jellema, W. T., Imholz, B. P. M., Van Goudoever, J.,
Wesseling, K. H. and Van Lieshout, J. J. (1996) Finger
arterial versus intrabrachial pressure and continuous
cardiac output during head-up tilt testing in healthy
subjects. Clin. Sci. 91, 193–200

10 Bos, W. J. W., Imholz, B. P. M., Van Goudoever, J.,
Wesseling, K. H. and Van Montfrans, G. A. (1992) The
reliability of noninvasive continuous finger blood pressure
measurement in patients with both hypertension and
vascular disease. Am. J. Hypertens. 5, 529–535
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W. J. A. (1985) Age-related changes in viscoelasticity of
normal and arteriosclerotic human aortas. In
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S. M. and Schneider, E., eds.), pp. 245–250, Martinus
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al. (1995) Beat-to-beat analysis of left ventricular
pressure–volume relation and stroke volume by
conductance catheter and aortic Modelflow in
cardiomyoplasty patients. Circulation 91, 2010–2017
Received 12 February 1999/15 April 1999; accepted 23 May 1999

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