Nephrol Dial Transplant (2001) 16: 595±603
Original Article
Prevention of haemodialysis-induced hypotension by biofeedback
control of ultra®ltration and infusion
Reinhard Schmidt1, Ottfried Roeher2, Heiko Hickstein1 and Steffen Korth3
1
Department of Internal Medicine, University of Rostock, Rostock, 2Dresden and 3Erfurt, Germany
Abstract
Background. Haemodialysis-induced hypotension is
still a severe complication in spite of all the progress
in haemodialysis treatment. Because of its multifactorial causes, haemodialysis-induced hypotension cannot
be reliably prevented by conventional ultra®ltration
and sodium pro®ling in open-loop systems, as they are
unable to adapt themselves to actual decreases in blood
pressure.
Methods. A blood-pressure-guided closed-loop system,
for prevention of haemodialysis-induced hypotension
by biofeedback-driven computer control of both ultra®ltration and saline infusion was clinically tested in
237 treatments of seven patients prone to hypotension.
As medical knowledge on multifactorial causes of
hypotension is characterized by a lack in deterministic
knowledge, fuzzy logic and linguistic variables were
used to involve clinical experience on hypotension
phenomena in terms of fuzzy knowledge. Biofeedback
control is based on frequent measurements of blood
pressure at 5 min intervals. Blood pressure behaviour
is described by linguistic variables and fuzzy sets.
Adaptive rule bases were used for the simultaneous
fuzzy control of both the ultra®ltration and infusion
of hypertonic saline (20% NaCl). Proper adaptation of
control features to patient's conditions was provided
by the critical borderline pressure, which was set by
the physician individually at the beginning of each
treatment. During the initial and medium phases of
the sessions, ultra®ltration rates up to 150% of the
average rates were applied as long as decreases in
blood pressure could be compensated by saline infusion. The surplus of ultra®ltrate volume was used for
blood pressure stabilization in the ®nal phase in most
instances by low ultra®ltration rates.
Results. The advantages of biofeedback-controlled
haemodialysis were demonstrated by both decreasing
the frequency of hypotonic episodes and by increasing
or maintaining constant levels of systolic blood
Correspondence and offprint requests to: Prof. Dr R. Schmidt, Klinik
fuÈr Innere Medizin, UniversitaÈt Rostock, Ernst-Heydemann-Str. 6,
D-18055 Rostock, Germany.
#
pressure during the ®nal phase in 88% of treatments.
As saline infusion was applied mainly in the initial
and medium phases, blood sodium levels were not
signi®cantly higher at the end of the sessions, and
interdialytic weight gain was not elevated.
Conclusion. The application of fuzzy logic in the
blood-pressure-guided biofeedback control of ultra®ltration and sodium infusion during haemodialysis is
able to minimize haemodialysis-induced hypotension.
Keywords: blood pressure; fuzzy control; haemodialysis; hypotension; infusion; ultra®ltration
Introduction
Symptomatic hypotension occurs in up to 30% of
haemodialysis treatments and represents one of the
most severe complications during haemodialysis treatment w1x. The causes of haemodialysis-induced hypotension are multifactorial. Inadaquate ¯uid removal,
drug intake, complications of the primary disease,
concomitant diseases, blood±membrane interactions
and others play a role w2±7x. These causes are known
qualitatively but there is a lack in understanding as to
what degree or quantity they contribute to hypotension w8±10x. Haemodialysis-induced hypovolaemia is
supposed to be a key parameter and its changes are
used to assess the cardiovascular situation of the
haemodialysis patient and to predict hypotensive
episodes. However, hypovolaemia is balanced by the
re®lling rate, peripheral vasoconstriction, increase of
heart rate, augmentation of venous return and release
of vasoacitve hormones. As hypovolaemia is compensated by different mechanisms, hypovolaemia alone
cannot be the leading parameter in assessing the
cardiovascular situation of the patient and it fails in
predicting hypotensive episodes w11x. All in¯uencing
parameters and mechanisms result in the actual blood
pressure and its course. The actual blood pressure
represents comprehensively the actual caradiovascular
situation of the patient. Therefore, the actual systolic
2001 European Renal Association±European Dialysis and Transplant Association
596
R. Schmidt et al.
blood pressure and its trend are the guiding parameters
for a biofeedback-driven monitor for blood pressure
stabilization during haemodialysis. Probabilistic reasoning and fuzzy logic were used to transfer medical
knowledge into a closed-loop system providing blood
pressure control in haemodialysis patients prone to
hypotension.
The most frequently used therapeutic interventions
in cases of haemodialysis-induced hypotension are infusion of volume, injection of hyperosmotic substances
(sodium 20%, glucose 40%), interruption of ultra®ltration and application of vasoactive drugs. By giving the
infusion of volume and interrupting ultra®ltration the
goal of ultra®ltration might not be reached. Repeated
injection of hypertonic saline could increase the
exchangable sodium pool and may result in thirst
and increased interdialytic weight gain. From former
studies w11,12x and from routine haemodialysis programmes we know that the ®rst half of the haemodialysis treatment shows much less hypotensive
episodes in comparison with the second half of the
treatment. In conclusion, it was obviously more bene®cial to ultra®lter in the ®rst part of haemodialysis as
much as the actual systolic blood pressure allows with
the consequence of low ultra®ltration rates at the end
of haemodialysis. In order to maintain maximum
ultra®ltration rates (MAX-rates) during the ®rst part
of haemodialysis, blood pressure can be additionally
stabilized by the injection of 20% saline. Sodium
application should be restricted to the ®rst half of
haemodialysis; a possible surplus of sodium can be
eliminated during the second half of the treatment. The
low ultra®ltration rates during the second half of
haemodialysis result in blood pressure stabilization
and the additional effect of sodium is unnecessary in
this phase of treatment.
(average 3.4"1.2 kg). Comparisons of interdialytic weight
gains after treatments with and without fuzzy-controlled
infusion were focused individually on the same patient during
the normal rhythm of 2±2±3 days weekly. For reliable results
only 2-day intervals were considered. Haemodialysis was
routinely performed with a high-¯ux dialyser. Bicarbonate
dialysate was used with a sodium concentration of 138 mmolul
and a potassium concentration of 2±4 mmolul. Dialysate
temperature in all treatments was 368C. Patients with vascular instability took their antihypertensive medication after
haemodialysis. All patients were allowed to eat and to drink
during haemodialysis.
Subjects and methods
Biofeedback control is provided by on-line transmission
of the crisp outputs to both the haemodialysis machine
(Dialog, B. Braun Melsungen) for ultra®ltration rate control
and to the programmable infusion pump (Perfusor secura
FT, B. Braun Melsungen) for infusion rate control.
As in most of the patients with vascular instability the
frequency of hypotensive events is increasing with ongoing
haemodialysis, the biofeedback control is focused on ultra®ltration rates as low as possible during the ®nal phase of
the session. This goal can be achieved by applying MAXrates up to 150% of the average ultra®ltration rate during
the initial and medium phases of treatment as long as it is
tolerated by the systolic blood pressure. In order to adapt
the control characteristics properly to the individual requirements of each patient, the critical borderline of systolic pressure (set point) is selected by the physician before starting the
treatment. Normally, set points of 90±100 mmHg are used
for patients having initial systolic pressures of 90 mmHg or
higher. For patients with initial systolic pressures -90 mmHg
the initial value itself is chosen as set point in most
cases. If the actual systolic blood pressure comes close to
the set point of 90 mmHg the automatic system reacts
®rst with injection of 20% saline to stabilize blood pressure
and in a second step if necessary with lowering ultra®ltration
rate.
Patients
Seven patients with vascular instability were selected to take
part in the study. Four were treated (97 treatments) with
fuzzy-controlled infusion of sodium chloride 20% depending
on the actual blood pressure and linear ultra®ltration. The
same four patients underwent in the second part of the
study fuzzy-controlled ultra®ltration pro®ling without sodium
infusion (60 treatments). All seven patients were treated with
fuzzy-controlled sodium infusion and fuzzy-controlled ultra®ltration pro®ling simultaneously in a third step (237 treatments). MAX-rates for ultra®ltration pro®ling were set to
140% (116 treatments) and ®nally to 150% (121 treatments)
of the average rate as usual during conventional haemodialysis
with linear ultra®ltration rate. Seventeen other patients out
of the routine haemodialysis programme served as a control
group and were treated with conventional haemodialysis.
The optimal weight of all patients is de®ned every 3 months
by assessing chest X-ray, tissue bioimpedance measurement,
blood pressure course and clinical signs. Myocardial function
in all patients was suf®cient (ejection fraction 43.6"8.2%).
The interdialytic weight gain differed from 1.6 to 6.1 kg
Methods
The closed-loop system for biofeedback control is shown in
Figure 1. The high reliability of biofeedback control is
maintained by non-invasive blood pressure measurements
via an arm cuff (Dinamap 1846 SX, Critikon, Norderstedt),
which are initiated automatically by the fuzzy controller at
5 min intervals. Three linguistic variables are calculated from
the measuring values: (i) relative difference of systolic
pressure and pre-adjusted set point pressure, (ii) short-term
pressure trend (15 min), and (iii) long-term pressure trend
(25 min). Each of the linguistic variables (i)±(iii) is de®ned by
speci®c fuzzy sets, which are described by trapezoid and
triangular membership functions for the interesting ranges of
the variable. Fuzzy logic is applied to the procedures of
biofeedback control in following steps:
. fuzzi®cation of input data by matching of actual
measuring values (i)±(iii) and relevant fuzzy sets inclusive
weighting of results by set operators;
. fuzzy inference by probabilistic reasoning extended to
speci®c rule bases for both control of ultra®ltration rate
and infusion rate of hypertonic saline solution; and
. defuzzy®cation of conclusions obtained from fuzzy
inference by conversion into crisp outputs for adaptation
of ultra®ltration rate and infusion rate to patient's actual
blood pressure behaviour.
Biofeedback control of ultra®ltration and infusion
597
Fig. 1. Closed-loop system for the simultaneous fuzzy control of ultra®ltration and infusion.
A MAX-rate of 150% of the average ultra®ltration rate
predetermined individually for each treatment was used in
121 treatments in the seven patients prone to develop
vascular instability during haemodialysis. Blood pressure
decreases below the set point during the initial and medium
phases of treatment were treated preferably by the biofeedback-controlled infusion of hypertonic saline (20% NaCl) to
maintain the ultra®ltration rate as long as possible at the
higher level.
The ultra®ltration rate was reduced only if the systolic
blood pressure could not be stabilized suf®ciently by saline
infusion. Vice versa, the biofeedback-controlled decrease
of the ultra®ltration rate was used preferably in the ®nal
phase of treatment to avoid saline infusion. Hypertonic
saline infused during the initial and medium phases will be
eliminated during the ®nal phase by a half-life of only
10±15 min by ongoing convective and diffusive mass
tranfer via the dialyser membrane. For this reason, no considerable increase of post-dialytic blood sodium is to be
expected from intradialytic saline infusion. Blood sodium
levels were measured at the beginning and after the end of
each session.
Results
Frequency of hypotonic intervals
In our previous studies w11,12x the frequency of
hypotensive episodes was considerably reduced in
patients prone to hypotension, if the biofeedbackdriven infusion of hypertonic saline (20% NaCl) was
used. However, decreasing trends of blood pressure in
the ®nal phase of treatment could not be avoided in
cases where the ¯uid transfer from both the intracellular space as well as the interstitium into the intravascular space is limited by re®lling rates which are too
low. Therefore, in the recent study, the blood-pressureguided fuzzy control of the ultra®ltration rate was
applied simultaneously with the automatic infusion of
20% NaCl.
Figure 2 shows a typical run where infusion was
necessary during the initial phase of the session only.
As a result of severe decreases in blood pressure in the
interval from 15 to 40 min the ultra®ltration rate was
reduced simultaneously. However, after stabilizing the
blood pressure the ultra®ltration rate automatically
increases again up to the MAX-rate. The total surplus
of ultra®ltrate volume achieved during the ®rst 2 h
of treatment enabled the ultra®ltration rate to be
reduced stepwise to only 463 mluh during the third
hour. The systolic blood pressure was reliably stabilized during the last 2 h above the set point pressure
(90 mmHg).
All of the treatments where hypotensive episodes
-90 mmHg occurred were analysed by recording the
measuring intervals (5 min) with low systolic pressure
(-90 mmHg). Each of the hypotonic intervals was
classi®ed by both its hour of occurrence and as the
level of blood pressure decrease (-60; 60 . . .-70;
70 . . . -80; 80 . . . -90 mmHg). The results were
compared with regard to four types of treatment:
(i)
conventional method of haemodialysis treatment
without fuzzy control (69 treatments);
(ii) fuzzy-controlled infusion of 20% NaCl and ®xed
ultra®ltration rate (97 treatments);
598
(iii)
fuzzy-controlled ultra®ltration pro®ling without
infusion (60 treatments); and
(iv) simultaneous fuzzy control of infusion and
ultra®ltration (45 treatments).
Figure 3 shows the frequency distributions of measuring intervals (5 min each) with low systolic pressure
versus the time of occurrence during haemodialysis
treatment. The ®gure illustrates, that the frequency of
low blood pressure situations under conventional
haemodialysis (®lled columns) increases almost linearly
during the treatment time course. Using only the fuzzycontrolled infusion of 20% saline (crossed columns) the
trend is similar but to a smaller extent. The fuzzycontrolled ultra®ltration pro®ling with a MAX-rate of
150% without infusion (hatched columns) shows an
increase of hypotensive episodes in the second hour but
a decrease of hypotension in the third and especially
in the fourth hour of treatment. The combination of
a fuzzy-controlled ultra®ltration with a MAX-rate of
150% and a fuzzy-controlled infusion of 20% NaCl
(dotted columns), results in the lowest levels for the
occurrence of hypotension. It can clearly be seen that
there is a stabilization of blood pressure in the second
half of haemodialysis (third and fourth hour).
Figure 4 illustrates the frequency of intervals with
low systolic blood pressure versus the level of blood
pressure decrease in the different types of treatment mentioned above. Conventional haemodialysis
shows the highest frequency of hypotensive intervals
with the lowest blood pressure levels, whereas the
fuzzy-controlled infusion of 20% NaCl and the
R. Schmidt et al.
fuzzy-controlled ultra®ltration also, achieve less
frequent hypotensive intervals and the extent of
hypotension was less severe.
The fuzzy-controlled infusion of 20% NaCl and
fuzzy-controlled ultra®ltration together show signi®cantly better results at all levels of blood pressure.
Blood pressure trend in the ®nal phase of
haemodialysis
The signi®cant progress obtained from biofeedbackcontrolled ultra®ltration with respect to blood pressure
behaviour in the ®nal phase of haemodialysis is shown
in Figure 5. The blood pressure trend during the ®nal
phase of haemodialysis (total time 4 h) was analysed
by comparing the mean systolic blood pressures during
the last (fourth) hour (BP4) and mean systolic blood
pressures during the third hour (BP3) for each individual treatment. Percental differences (BP4 BP3)uBP3
were calculated and classi®ed by steps of 5% each. The
results from conventional haemodialysis with linear
ultra®ltration were compared with (i) fuzzy-controlled
infusion and linear ultra®ltration, (ii) fuzzy-controlled
ultra®ltration (MAX-rate 150%) without infusion, and
(iii) simultaneous fuzzy control of both ultra®ltration
(MAX-rate 150%) and infusion.
As shown in Figure 5, the frequency distributions
of fuzzy-controlled groups (i)±(iii) are characterized by
signi®cantly better locations in comparison with conventional haemodialysis. Only from 32.4% of conventional treatments (black columns) values (BP4 BP3)u
BP3P0% were obtained. That means, in only 32.4% of
Fig. 2. Simultaneous fuzzy control of ultra®ltration and infusion. BP, systolic blood pressure; SP, set point pressure; UFR, ultra®ltration
rate; UFRav, average ultra®ltration rate; PR, infusion rate; PRmax, maximum infusion rate.
Biofeedback control of ultra®ltration and infusion
599
Fig. 3. Frequency distributions of intervals with low systolic blood pressure versus time of occurrence.
conventional treatments the mean systolic pressure
BP4 was higher than the mean systolic pressure BP3
during the preceding hour, or at least equal to BP3. In
group (i), fuzzy-controlled infusion and linear ultra®ltration (crossed columns), this number was elevated
to 44.4% of treatments, which met this criterion. In
group (ii), fuzzy-controlled ultra®ltration without
infusion (hatched columns), a high majority of 81.7%
of treatments complied with values (BP4 BP3)u
BP3P0%. However, additional progress was obtained
from group (iii), simultaneous fuzzy control of ultra®ltration and infusion (dotted columns), where 88.4%
of treatments met this criterion.
Hypertonic saline infusion and post-haemodialysis
blood sodium
The amounts of hypertonic saline infused during the
treatments were analysed separately for each hour as
shown in Figure 6. The signi®cant different trends of
saline infusion in the last 2 h of treatment demonstrate
clearly the essential effects of fuzzy-controlled ultra®ltration. As visible from the series of 97 treatments
(four patients) with ®xed ultra®ltration rates during
the entire session, an increasing volume of hypertonic
saline solution was necessary to stabilize the blood pressure under ongoing haemodialysis if fuzzy-controlled
ultra®ltration was not available. The volume of saline
infusion was elevated progressively from 8.4 ml during
the ®rst hour of treatment to 37.8 ml in the ®nal hour,
i.e. 450% of the ®rst value.
Considering the group of 82 treatments (seven
patients) with fuzzy-controlled ultra®ltration and infusion of 20% NaCl, the distribution of saline infusion
shows during the ®rst 2 h a very similar behaviour like
the series mentioned above as in this phase the ultra®ltration rate is kept at the MAX-rate preferably.
However, the new quality of fuzzy-controlled ultra®ltration is characterized by a systematic decrease of
saline infusion after the second hour of the treatment.
In this phase the ultra®ltration rate is reduced automatically by the biofeedback control system because of
the surplus of ultra®ltrate volume accumulated by the
MAX-rate during the ®rst half of the session. The ultra®ltration rate is decreased stepwise to a very low level.
In the ®nal phase of the session -40% of the average
ultra®ltration rate, as predetermined by the physician
for the entire session, will be achieved (Fig. 2). With
respect to the post-dialytic level of blood sodium it is
highly important that saline infusion decreased from
12.0 ml during the second hour of the sessions to only
5.6 ml during the ®nal hour. In contrast, an increase
up to 37.8 ml was necessary if fuzzy-controlled
ultra®ltration was not available. Thus, saline infusion
600
R. Schmidt et al.
Fig. 4. Frequency distributions of hypotonic intervals versus levels of systolic blood pressure.
Fig. 5. Frequency distribution of systolic blood pressure in the ®nal phase of treatment. BP4 and BP3, mean systolic blood pressure during
the fourth (BP4) and the third hour (BP3).
Biofeedback control of ultra®ltration and infusion
601
Fig. 6. Distribution of hypertonic saline infusion (20% NaCl) during haemodialysis treatment using simultaneous fuzzy control of
ultra®ltration and infusion.
in the ®nal hour of treatment was reduced from
37.8 ml (100%) to -15% (5.6 ml) if fuzzy-controlled
ultra®ltration was applied simultaneously. Blood
sodium levels were measured at beginning and at the
end of these sessions (Table 1). The average levels of
post-dialytic blood sodium after the simultaneous
infusion of 20% saline for the individual patients
and for seven patients altogether result in slightly
higher values only (139.4 mmolul) in comparison with
the average levels of the pre-dialytic measurements
(137.9 mmolul). There were also small differences
only in post-dialytic blood sodium between sessions
with (139.4 mmolul) and without (138.0 mmolul) saline
infusion.
These results agree with statistical results from
correlation analysis and linear regression of treatments
with simultaneous fuzzy control of both ultra®ltration
and saline infusion. The correlation r between postdialytic blood sodium and saline volume infused
during the ®rst to third hour of treatment has proven
non-signi®cant (r-0.1; P)0.05) as a result of the
short saline infusion half-life of about 15 min during
haemodialysis. Alternatively, a highly signi®cant correlation r was found between the blood sodium and
saline volume infused during the last (fourth) hour of
treatment (r)0.5; P-0.001). However, the very low
ultra®ltration rates in the ®nal phase, as provided by
fuzzy-controlled ultra®ltration, require extremely small
volumes of saline infusion during the last (fourth) hour
of treatment.
Thus, patient's interdialytic weight gains were not
signi®cantly affected by fuzzy-controlled saline infusion during treatments with simultaneous fuzzy control
of ultra®ltration.
Discussion
Patients on regular haemodialysis treatment are getting
older, and simultaneously their time on a regular haemodialysis programme is increasing. In particular patients
suffering from long-term hypertension or diabetes
mellitus develop haemodialysis-induced hypotension
during haemodialysis treatment. From fundamental
publications w13±16x it is known that most complicationsÐespecially hypotensive episodesÐduring haemodialysis are multifactorial and are caused by different
mechanisms. Changes in plasma volume caused by
ultra®ltration and time variance of ¯uid shifts between
the compartments of the body are considered as important factors w17,18x. Autonomic neuropathy may be
602
R. Schmidt et al.
Table 1. Blood sodium levels pre- and post-haemodialysis
Patient
A. L.
H. B.
I. W.
Four patients
All seven
patients
Haemodialysis
sessions
20% NaCl infusion
average (ml)
32
15
36
10
10
9
4
5
25.7
0 (no
43.6
0 (no
25.9
0 (no
37.8
0 (no
82
39
34.3
0
infusion)
infusion)
infusion)
infusion)
responsible for the limitation of vascular stability w19x.
Depletion of vasoactive substances and acid±base
changes are in discussion. Physical training, drug
intake and food uptake can modify patients shape.
Finally, the biocompatibility of haemodialysis membranes and blood temperature during haemodialysis
play a certain role in initiating clinical complications.
All these factors can in¯uence blood pressure behaviour during haemodialysis. If hypotension occurs the
symptom `collapse' is treated symptomatically. Volume
substitution, injection of osmotic substances, increasing
of dialysate conductivity, decrease of ultra®ltration to
zero, diminution of speed of the blood pump and
administration of vasoactive drugs are methods proven
in clinical practice to treat acute hypotension during
haemodialysis. In order to prevent hypotensive episodes
during haemodialysis, ultra®ltration and sodium pro®les
have been developed.
However, clinical experience shows that therapeutic
methods as mentioned above are of limited therapeutical effect in treating patients with vascular
instability during haemodialysis, as actual changes in
blood pressure behaviour are not considered continuously. Reliable prevention of haemodialysis-induced
hypotension is achievable only from biofeedbackdriven closed-loop systems guided by frequent blood
pressure measurements. As medical knowledge on the
multifactorial causes of hypotension is characterized
by a major lack in deterministic knowledge, the use of
scienti®c approaches like fuzzy logic is necessary to
involve clinical experience in terms of fuzzy knowledge.
The advantages of preventing haemodialysis-induced
hypotension by blood-pressure-guided closed-loop
systems are proven by the results from the biofeedback-driven fuzzy control of ultra®ltration and saline
infusion.
Conclusions
The simultaneous computer control of ultra®ltration
and the infusion of hypertonic saline have proven the
Average blood sodium (mmolul)
Pre-haemodialysis
post-haemodialysis
136.3
137.2
139.2
138.5
137.5
137.4
140.0
141.6
138.8
137.4
139.4
136.6
140.4
137.9
142.5
141.5
137.9
138.2
139.4
138.0
most effective means for automatic blood pressure
stabilization during haemodialysis treatment.
Prevention of hypotensive events can be optimized
obviously, if speci®c modes of biofeedback control are
used in the initial, medium, and ®nal phases of the
sessions. To achieve a high surplus of ultra®ltrate
volume in the initial and medium phases, decreases in
blood pressure should be compensated during these
phases by saline infusion. Because of remarkably
reduced re®lling rates in many patients during the
®nal phase of treatment, automatic blood pressure
stabilization should be dominated by ultra®ltration
rate control in this phase.
As MAX-rates rates up to 150% of the average
ultra®ltration rate were tolerated well by all patients
involved in the clinical tests, MAX-rates of 150% are
recommended for most haemodialysis patients in the
interest of low ultra®ltration rates in the ®nal phase, if
the blood-pressure-guided biofeedback control of
ultra®ltration is used.
Session goals regarding the total weight loss were
achieved in all cases, although ultra®ltration rates
could be diminished by biofeedback control in the
®nal phase to -40% of the average ultra®ltration rate
because of the surplus accumulated during the initial
and medium phases.
Fuzzy-controlled ultra®ltration is preventing sodiumcorrelated complications during the interdialytic phase
as saline infusion is minimized in the ®nal phase of
treatment. Saline infusions in the initial and medium
phases obviously do not affect the post-dialytic blood
sodium level because of the saline infusion half-life of
about 15 min only during ongoing haemodialysis
procedure.
Fuzzy control is reproducible at any time during
haemodialysis treatment as fuzzy knowledge is processed by strictly de®ned fuzzy sets, operators and rules.
Patients feel better monitored and staff appreciate
biofeedback-controlled haemodialysis.
Acknowledgement. Authors express their gratitude to B. Braun
Melsungen for supporting this work.
Biofeedback control of ultra®ltration and infusion
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Received for publication: 9.4.99
Accepted in revised form: 17.10.00