Confidence limits of arteriovenous fistula flow rate measured by

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					Nephrol Dial Transplant (2003) 18: 955–960
DOI: 10.1093/ndt/gfg075

Original Article

Confidence limits of arteriovenous fistula flow rate measured by the
‘on-line’ thermodilution technique

Joe L. Ragg, John P. Treacy, Paul Snelling, Melinda Flack and Sonia Anderton

Northern Territory Clinical School, Flinders University, Royal Darwin Hospital, Northern Territory, Australia

Abstract                                                               Introduction

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Background. A method is presented for estimating the
confidence limits (CLs), or accuracy, of the arterio-                   Major consensus guidelines have recommended the
venous fistula flow rate measured at haemodialysis by                    measurement of the flow of arteriovenous fistulae as the
the ‘on-line’ thermodilution technique.                                preferred means of monitoring their function, along
Methods. This was by derivation of an expres-                          with physical examination [1,2]. Specifically, investiga-
sion to estimate what variance a set of repeated mea-                  tion of fistulae is recommended where flow rate is below
sures of flow would yield, using values pertaining                      a particular threshold (500 and 600 mlumin in native
to a single measure of flow. (Laws of variance were                     and graft arteriovenous fistulae, respectively), or where
applied to the formula used to calculate flow, to                       there is a fall in flow rate (20–25% or more from baseline
account for its variables’ values and measurement                      in either of these fistulae).
errors.) This enabled CLs of a single measure to be                       There is expectation that ‘on-line’ techniques of
estimated.                                                             measuring flow rate will supplant others in enabling
Results. The variance estimated from a single measure                  ‘accurate and inexpensive repetitive measurements’ [1].
was compared with that actually observed upon imme-                    A number of reports have validated flow rates measured
diately taking a second measurement; differences in                    by such methods [3–9], and others have identified fac-
189 pairs were not significantly different from zero                    tors that will compromise its accuracy [4]. However, no
(Ps0.56). Applying the results demonstrated that                       study has aimed solely to describe confidence limits
measured flow values of 430–570 mlumin typically had                    (CLs) of measured flow, which are an easily understood
associated 95% CLs that included 500 mlumin; there-                    and clinically applicable expression of measurement
fore, true flow could not be said to be either side of                  accuracy. Knowledge of the accuracy of on-line flow
500 mlumin. The same was the case for 500–700 mlumin                   measurements is of clinical significance, as interven-
with regard to 600 mlumin. CLs widened considerably                    tion is recommended based on the value of these
with the magnitude of flow rate, limiting the accurate                  measurements.
measurement of higher flows and the detection of                           The aims of this study were to describe a method to
falls in flow.                                                          estimate the CL of access flow rate as measured by the
Conclusion. A method to estimate CLs of flow rate                       ‘on-line’ thermodilution technique, and to apply this to
                                                                       clinical decision making when assessing arteriovenous
measured by the thermodilution technique is presented
                                                                       fistulae and grafts.
and validated. Application demonstrates an accurate
measurement of low flow, but limitations at higher flow
and in detecting falls in flow. Appreciating the magni-
tude of such is critical to informed clinical decision                 Subjects and methods
making when using flow rate in an access surveillance
                                                                       Patients participating were all those attending a satellite
programme.                                                             dialysis centre of a teaching hospital for stable chronic
                                                                       haemodialysis patients.
Keywords: access flow; accuracy;                  haemodialysis;
thermodilution; vascular access
                                                                       Flow measurement technique
                                                                       Flow rate (Q) was measured by the ‘on-line’ thermodilution
Correspondence and offprint requests to: Dr J. L. Ragg, 26 Learmonth   technique, as described and validated by Schneditz et al. [8].
Street, Ballarat, Victoria 3350, Australia.                            This requires the substitution of the equation given for
Email:                                              cardiopulmonary recirculation (Equation 6 in Schneditz et al.

#   2003 European Renal Association–European Dialysis and Transplant Association
956                                                                                                                      J. L. Ragg et al.
[8]) into the equation given for flow rate (Equation 4 in            variable’s measurement error). The UFR was kept as a
Schneditz et al. [8]). The resulting formula consists of five        constant value. Variables were re-allocated randomly to each
component variables:                                                other, and 10 000 Q values were generated from these.
         ð1{RxÞðQx{UFRÞ                                                Table 1 demonstrates the results. First, the distributions
Q~ n        h                    io                          ð1Þ    yielded were not normal in nature. However, their inverse
       Rx(1{ (RnððRxð1{RnÞQnÞ Þ)                                    transformations approximated the normal (kurtosis near to
                                                                    3, and skewness near to 0). Secondly, SDs of the distributions
where Rn and Rx are the recirculation of dialysis lines in the      were not constant (they increased with the median flow rate
usual and transposed positions, respectively; Qn and Qx are         of the Q distribution, or vice versa for their inverse trans-
the extracorporeal blood flow rate, concurrent with the above        formations). Figure 1 illustrates the distributions obtained
Rn and Rx readings, respectively; and UFR is the ultrafiltra-        relevant to the patient with a flow rate lying on the 50th
tion rate (constant throughout the whole flow measurement).          percentile of all observed.
   The technique is invalid where there is recirculation in the
fistula. Therefore, where Rn values were )15% [10],
measurements were excluded from analysis. Nonsensical read-         Estimation of the confidence limits of measured flow rate
ings (arbitrarily those )6.5 lumin or negative flows) were also      The 95% CLs of a single flow (Q) measure can be calculated as
excluded. These arise from very low recirculation measures          being 1.96 standard measurement errors either side of a single
with lines in the transposed position, raising the possibility      measure, assuming that the distribution of repeated measures
that the venous needle is not directly downstream of the            is normal in nature. Table 1 demonstrates that such a
arterial needle, e.g. in a collateral vein coming off upstream      distribution is not normal in nature (see above), but that the
of the arterial needle or in a separate vein all together.          inverse transformation, invQ, with a corresponding SD of SD

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   Pairs of flow readings were taken, as per the following           invQ reasonably approximates normal (kurtosis near to 3, and
approach. In the first hour of dialysis, a pair of Rn readings       skewness near to 0). The CLs calculated instead for invQ are
was recorded, along with the concurrent Qn (as per machine          valid. CLs on the scale of Q can then be calculated by:
digital display). Lines were transposed and, similarly, a pair of
Rx and the concurrent Qx were recorded. The UFR (as per             95% CLs for Q~                                             ð2Þ
machine digital display), constant throughout all measure-                            ½invQ+1:96|SD invQŠ
ments, was recorded. Two flow rates were calculated according          As is also demonstrated in Table 1, SD invQ is not
to Equation 1, using the first value in each pair, and then          constant. Specifically, it decreases with increasing magni-
the second, along with the constant UFR. This was an                tude of flow rate. Therefore, an expression is required for
approximation to taking two immediately sequential flow              substitution into Equation 2. The variance of the general
readings (i.e. the need to transpose lines repeatedly, thereby      function y, of the random variables x1, x2, x3. . . whose
subjecting the patient to a small but theoretical risk of cross-    variances are known, and where each x is independent of
infection was avoided).                                             the other, can be approximated by
   All measurements were performed using Fresenius 4008B
dialysis machines fitted with a blood thermodilution monitor                      varð yÞ~½y’ðx1ފ2 |varðx1Þz½y’ðx2ފ2
(BTM). Arterial needles faced the anastomoses and were as                                |varðx2Þz½y’ðx3ފ2 |varðx3ފz . . .
near to it as possible. Vascular access was obtained with 14-
gauge arterial and venous needles and Fresenius blood lines.        where: y9(x1): is the partial derivative of y with respect to x1,
                                                                    etc.; var (x1) is the variance of x1, etc.; and the expression is
                                                                    calculated at the mean of each x.
Measurement error of recirculation and extracorporeal                  Analogously, the function invQ is of the variables Rn, Rx,
blood flow rate                                                      Qn and Qx whose variances (measurement error) are known,
                                                                    each of which is independent of the others. Values can be
Recirculation as measured by the BTM has been validated             substituted accordingly to yield an expression for the variance
elsewhere [11]. In this study, measurement accuracy of              of the invQ function (and therefore its standard deviation, SD
recirculation was assumed to be reflected by the immediate           invQ). A qualification is that the expression is not calculated at
reproducibility of the measure, and this was quantified by           the mean or true values of each variable (see Appendix). For
considering the SDs of small sets (pairs) of recirculation          simplicity, the measurement error of UFR is not discussed,
measures. The pairs of recirculation measures were recorded
as per the flow measurement technique above, and the
measurement error of recirculation was taken as the median          Table 1. Summary of the distributions representing repeated mea-
of all SDs calculated.                                              sures of flow rate (computer simulation) for those patients whose
   For the purposes of this study, a measurement error of 4%        flow rate lay on the 10th, 30th, 50th, 70th and 90th percentiles of all
                                                                    those measured (with the inverse transformation also shown)
coefficient of variation for extracorporeal blood flow rate
was assumed (see Discussion) [12], and this was assumed to
                                                                    Percentile      Q (mlumin)      SD           Skewness        Kurtosis
be unaffected by access flow rate.
                                                                    10th             438             40          0.40             3.28
Computer simulation of repeated measures of flow rate                30th             708             72          0.47             3.56
                                                                    50th             906            112          0.68             4.03
A computer simulation of repeating flow measurements                 70th            1192            178          0.95             5.42
10 000 times, in those patients whose fistula flow rate lay on        90th            1862            419          1.66            10.42
the 10th, 30th, 50th, 70th and 90th percentiles of those            10th   Inv      0.0023          0.00021      0.14             2.97
measured, was undertaken. This was by noting the value of the       30th   Inv      0.0014          0.00014      0.17             3.11
variables used to calculate flow at the particular percentile,       50th   Inv      0.0011          0.00013      0.09             2.99
and generating sets of 10 000 such variable values (the mean        70th   Inv      0.0008          0.00012      0.10             3.13
                                                                    90th   Inv      0.0005          0.00010      0.07             3.07
being the originally noted value, with spread equal to that
CL limits of AV fistula flow rate measured by ‘on-line’ thermodilution                                                                957

Fig. 1. The distribution of repeated flow rate measurements obtained by computer simulation, relevant to the patient with the flow rate of
906 mlumin (which lay on the 50th percentile of all flow rates observed): (A) the usual and (B) with inverse transformation.

and could be made zero by setting UFR to zero during flow               248 mlumin (IQR 232–277) and UFR 760 mluh (IQR
measurements.                                                          555–900), and the calculated flow was 919 mlumin (IQR
   Finally, the measurement error of recirculation can be              657–1254).

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lessened by taking two immediately sequential measures and
averaging these (lessened to a new value of ‘measurement
                                                                       Correlation of repeated flow measures
error’ud2, the standard error of a mean of two values). Herein,
CLs for flow rate, where flow rate is calculated using such              There was good correlation between repeated measures
values, are referred to as CL2, whereas in the instance of using       of flow rate (Ts0.68, P-0.001) although the
just single measures of recirculation, they will be referred to as     repeatability lessened considerably with increasing
CL1.                                                                   magnitude of flow rate. This is illustrated in Figure 2.
                                                                       Measurement error of recirculation and extracorporeal
Ethical approval was granted by the Top End Human
Research Ethics Committee.                                             blood flow rate
                                                                       The magnitude of difference within Rn pairs was not
Statistical analysis                                                   related to its averaged value (Ts0.03, Ps0.55). It was
                                                                       related for Rx pairs (Ts0.14, Ps0.006), but to a
Values were expressed as median (IQR, interquartile range).            relatively small real extent only (Table 2). The median
Correlation of continuous variables was tested by Kendall’s            SD of all Rn pairs was 1.48, and of all Rx pairs was
rank correlation coefficient (T). The null hypothesis that              1.41.
differences between matched pairs is zero was tested by the
Sign test. Statistical analysis was carried out using STATA
7.0 statistical software. Significance was considered as                Confidence limit of a measured flow rate
P-0.05.                                                                Equation 3 estimates the variance that repeated mea-
                                                                       sures of invQ would have by using variables pertaining
Results                                                                to a single measure of flow. This is to enable the
                                                                       calculation of confidence limits of a single measure of
There were 56 patients studied (and 56 fistulae). They                  flow according to Equation 2. To test this, variables and
were of age 51 years (IQR 46–59) and 35 were female.                   their measurement error relevant to the calculation
All fistulae were native, although two were interposi-                  of the first Q in each of the 189 pairs were substituted.
tion vein grafts. Arteriovenous anastomoses were at
the anatomical snuffbox in 21, the other distal quarter
radial artery in 16, the proximal three-quarters radial
artery in one, and the brachial artery in 18.
   There were 197 pairs of measures taken. Six were
excluded from analysis because of nonsensical flow
readings (see Methods above). A further two were also
excluded from analysis because of clearly discrepant or
‘outlier’ Rx pair measurements. These Rx readings were
41.0 and 15.4%, and 52.1 and 14.1%; the cause for these
was unclear. Thus 189 pairs of readings were analysed,
at three (IQR 2–5) measures per patient.
   The summary statistics for variables measured to
calculate flow, were Rn 7.7% (IQR 6.0–9.7), Rx 25.4%
(IQR 20.9–30.9), Qn 275 mlumin (IQR 240–283), Qx                       Fig. 2. Correlation of immediately sequential flow measurements.
958                                                                                                                   J. L. Ragg et al.
Table 2. The standard deviation of a pair of Rx measurements

Average                       n                       Median SD

-20                           43                      1.34
20–30                         94                      1.41
30–40                         37                      1.41
40–50                         11                      2.12
)50                            4                      2.05

The median values of all those calculated are tabled in groups
according to the average value of the Rx pair.

Table 3. Confidence limits of the measured flow rates that lay on a
selected percentile of all measured

Percentile    Flow (mlumin)        CL1 (mlumin)a   CL2 (mlumin)a
                                                                     Fig. 3. Observed flow rates up to 2500 mlumin, and their estimated
 5             306                  265–361         272–349          CL2 limits.
10             438                  373–532         384–510

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20             599                  504–739         521–707
30             709                  593–883         614–839          Table 4. Flow rate example (Q) and values 20% less, and the flow
40             808                  659–1044        686–982          rates whose estimated CL2 values lay immediately next to these
50             908                  738–1179        770–1107         values
60            1016                  815–1348        854–1254
70            1192                  938–1636        988–1503         Q (CL2)               Q         Q less 20%       Q (CL2)
80            1375                 1066–1938       1129–1760
90            1857                 1352–2964       1453–2572
95            2475                 1588–5613       1747–4242          696   (600–829)       600       480              405   (356–471)
                                                                     1093   (906–1378)      900       720              614   (532–727)
a                                                                    1621   (1193–2529)    1200       960              762   (644–945)
 CLs estimated according to Equation 2, where either single
measures of Rn and Rx (CL1), or two measures each of Rn and          1955   (1492–2835)    1500      1200              946   (776–1211)
Rx were taken and averaged (CL2), before substitution to calculate   2591   (1876–4187)    1800      1440             1084   (867–1446)
the access flow rate by Equation 1.

The differences between the variance estimated by                    values, and their values minus 20%, with the measured
Equation 3 and that actually observed in all 189 pairs               flow rates whose estimated upper or lower CL2 limits
were not significantly different from zero (Ps0.56).                  lay immediately nearest these values. It demonstrates,
                                                                     for example, that falls from a measured 696 to
                                                                     405 mlumin, or 2591 to 1084 mlumin are required to
Examples of practical application
                                                                     indicate a true 20% fall in flow rate.
There was considerable widening of CLs of the
measured access flow rate, or a lesser reproducibility
of measurement, with increasing access flow rate. This                Discussion
is demonstrated in Table 3, which gives flow rates lying
on various percentiles of all those measured, along                  The main findings from this study were the increasing
with their estimated CL1 and CL2 values. This is also                width of the CLs with higher flow rates, as shown in
demonstrated in Figure 2, which shows graphically the                Table 3, consistent with there being a much lesser
immediate reproducibility of access flow rate measure-                repeatability of measure in patients with higher fistula
ments, and Figure 3 which demonstrates graphically                   flow rates, as shown in Figure 2. As demonstrated, it is
all flow rate measurements with estimated CL2 values.                 both the value of, and the measurement error of, the
   The observed flow rates with estimated upper or                    component variables of the equation to calculate flow
lower CLs (CL2) nearest 500 mlumin were 427 mlumin                   rate, along with the mathematical properties of the
(372–499) and 559 mlumin (491–649), respectively, which              equation used to calculate flow rate, that ultimately
indicates that a measured flow rate of ;430–                          determine the ‘measurement error’ or repeatability of
570 mlumin will indeterminately classify the true access             the calculated flow rate. Whilst measurement errors of
flow rate to be either side of a 500 mlumin threshold.                the component variables of the equation to calculate
Similarly, for a 600 mlumin threshold, flow rates with                flow rate are constant across access flow rates,
estimated CL2 limits of 529 mlumin (459–625) and                     ‘measurement error’ of the calculated flow rates is not.
709 mlumin (614–839) indicate that a measured flow rate               It increases with access flow rate in a somewhat
of ;500–700 mlumin will indeterminately classify the                 exponential fashion. It is this, rather than a physiolo-
true flow rate to be either side of a 600 mlumin threshold.           gical phenomenon, that explains the increasing ‘mea-
   Very large falls in measured flow rate need to occur to            surement error’ of calculated access flow rate with
determine a true 20% fall in flow rate, particularly falls            access flow rate by the ‘thermodilution technique’. Such
from the higher flow rates. Table 4 gives arbitrary Q                 a pattern has been noted previously, but not quantified;
CL limits of AV fistula flow rate measured by ‘on-line’ thermodilution                                                          959

Schneditz et al. [8] noted that paired readings obtained               blood flow rates have been shown not to be perfectly
by the on-line thermodilution method had ‘good                         accurate. There is limited literature pertaining exclu-
correlation’ only to flows of 1.5 lumin.                                sively to the Fresenius machines. Sands et al. [12]
   Also of note is the eccentric placement of the CLs                  compared extracorporeal flow rate displayed on the
about the Q value. This is consistent with the skew                    Fresenius 2008H machine with readings obtained by
distribution that results from repeated measures of Q,                 an ‘on-line’ sensor of extracorporeal blood flow
as demonstrated in Table 1 and Figure 1.                               (Transonic2 haemodialysis monitor). The flow rate
   There is some consensus that the optimal access flow                 displayed slightly overestimated flow in comparison
rate thresholds indicating impending native and graft                  with the on-line sensor, with a measurement error
fistulae dysfunction are 500 and 600 mlumin, respectively               coefficient of variation of ;5–6%. The measurement
[2]. This study indicates that measured flow rates of                   error may have been overestimated, as there must be at
430–570 mlumin and 500–700 mlumin indeterminately                      least some measurement error associated with the
classify access flow rate either side of these thresholds.              Transonic2 haemodialysis monitor against which it
Therefore, to justify fistulae intervention upon obtaining              was compared. Furthermore, intra-patient measure-
                                                                       ment errors were not reported. Conceivably, these could
flow measures within these ranges, even greater import-
                                                                       be less than the values reported, which were for all
ance needs to be placed on corroborating clinical and                  patients’ measures combined.
surveillance method evidence of impending fistula                          The reproducibility of flow measurement by the
dysfunction.                                                           thermodilution technique has been expressed by

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   There is consensus that a fall in access flow rate of                Schneditz et al. [9] as the mean difference between
20–25% or more is indicative of impending fistula                       pairs of readings. This was 26"298 mlumin (ns52).
dysfunction [2]. For practical purposes, this study indi-              However, this summary statistic does not account
cates that the thermodilution technique of measuring                   specifically for the lesser reproducibility at higher flow
access flow rate has limited sensitivity in detecting such              rates. Nor was it clear if in the calculation of flow, the
falls, particularly as mentioned in the Results, from the              recirculation measures were a single measure or the
higher access flow rates.                                               average of a pair. In the same paper, flow rate estimated
   While flow measurement increasingly is recom-                        by the ultrasound dilution technique gave a slightly
mended as the preferred method of surveillance of                      better reproducibility of 27"212 mlumin. Our value,
arteriovenous fistulae function, there is limited litera-               calculated in the same way, using single recirculation
ture pertaining to the measurement error of recircula-                 measurements to calculate flow was less reproducible at
tion, extracorporeal blood flow rate and fistula flow                     10"453 mlumin.
rate measured by the thermodilution technique and, to                     Also of relevance to the ultrasound dilution tech-
some extent, by other methods.                                         nique, an in vivo validation [3] expressed reproducibility
   Regarding recirculation by the thermodilution tech-                 of flow rate as the coefficient of variation (SDumean) of
nique, Schneditz et al. [9] have expressed reproduci-                  46 sets of five consecutive measures, and this was
bility as the difference between paired readings. This                 13.4"6.4%. There was no significant difference across
was À0.4"1.84% (ns52) for Rn readings and À0.29"                       three brackets of flow magnitude. In this study, with
3.26% (ns54) for Rx readings. Our values, calculated                   single measures of variables to calculate flow rate, this
by the same method, were less reproducible at 0.00"                    was less at 16.2"14.6%. As expected, the reproduci-
3.26% and 0.00"3.46%, respectively. Wang et al. [10]                   bility was better at lower flow rates. Across three equal
expressed the reproducibility as the relative deviation                centile brackets of flow rate, these were 12.2"9.9,
from the mean of two consecutive measures, (R1–R2)                     16.1"11.6 and 20.0"19.1%. This would suggest that
3 100u(mean of R1 and R2), and for Rn and Rx readings                  the accuracy of measurement by the thermodilution
combined this was 2.5"11.5% (ns220). Our value,                        technique is comparable with that by the ultrasound
calculated in the same way, was less reproducible at                   dilution technique. This is so particularly at the more
À1.1"33.3%.                                                            critical lower flow rates, and where two recirculation
   Another independent dialysis unit reported a similar                measures are taken and averaged before entering into
measurement error using a similar machine and BTM                      the equation to calculate flow rate (see the improvement
monitor: a median SD of 1.63 (ns97) and 1.34 (ns97)                    in CL2 over CL1 (Table 3).
for Rn and Rx pairs of readings, respectively (D.
Bolsch, Hartley Dialysis Center Adelaide, Australia,
personal communication).                                               Conclusion
   Relevant to the ultrasound dilution technique of
measuring recirculation, Depner et al. [14] described                  This study presents and validates a method to estimate
the reproducibility of Rx measures by the Pearson                      confidence limits of flow rate measured by the thermo-
correlation coefficient and the mean absolute error of                  dilution technique. Application demonstrates reason-
paired readings as 0.98, 3.9"2.8%, which was similar                   ably accurate measurement of low flow, but limitations
to that calculated for this study (0.92, 2.6"2.4).                     at higher flow and in detecting falls in flow, and
   Regarding the measurement error of extracorporeal                   awareness of this is critical to informed clinical decision
blood flow rate, the Fresenius 4008B machine gives a                    making where using flow rate in access surveillance
digital readout of Qn and Qx. Displayed extracorporeal                 programmes.
960                                                                                                                       J. L. Ragg et al.

Appendix                                                               3. Bosman PJ, Boereboom FT, Bakker CJ et al. Access flow
                                                                          measurements in hemodialysis patients: in vivo validation of an
                                                                          ultrasound dilution technique. J Am Soc Nephrol 1996; 7: 966–969
The true mean or true value of each of the variables                   4. Krivitski NM. Theory and validation of access flow measure-
used to calculate flow are not known, and therefore                        ment by dilution technique during hemodialysis. Kidney Int 1995;
conditions for applying Equation 3 are not fully met.                     48: 244–250
The effect on the accuracy of the calculated CLs was                   5. Lindsay RM, Blake PG, Malek P et al. Hemodialysis access
investigated as follows.                                                  blood flow rates can be measured by a differential conductivity
                                                                          technique and are predictive of access clotting. Am J Kidney Dis
   The true flow rate should in 95% of instances be
                                                                          1997; 30: 475–482
contained within the 95% CLs.                                          6. Lindsay RM, Bradfield E, Rothera C et al. A comparison of
   Consider again the aforementioned computer simula-                     methods for the measurement of hemodialysis access recircula-
tion, of taking 10 000 consecutive flow rates in the                       tion and access blood flow rate. ASAIO J 1998; 44: 62–67
patients whose flow rate lay at the 10th, 30th, 50th, 70th              7. Lindsay RM, Blake PG, Malek P et al. Accuracy and precision
and 90th percentiles of all flow rates measured. A                         of access recirculation measurements by the hemodynamic
random sample of 1000 from each was taken. The CL                         recirculation monitor. Am J Kidney Dis 1998; 31: 242–249
for each of these flow rates was calculated according to                8. Schneditz D, Fan Z, Kaufman A, Levin NW. Measurement of
Equation 2. The ‘true’ flow rate (median flow rate of the                   access flow during hemodialysis using the constant infusion
                                                                          approach. ASAIO J 1998; 44: 74–81
overall distribution) was outside the relevant CL in 202
                                                                       9. Schneditz D, Wang E, Levin NW. Validation of haemodialysis
of the 5000 (4.0%) instances. This would validate the                     recirculation and access blood flow measured by thermodilution.
calculation of the CLs according to Equations 2 and 3

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                                                                          Nephrol Dial Transplant 1999; 14: 376–383
as being reasonable despite the conditions for applying               10. Wang E, Schneditz D, Kaufman AM, Levin NW. Sensitivity and
Equation 3 not being fully met.                                           specificity of the thermodilution technique in detection of access
                                                                          recirculation. Nephron 2000; 85: 134–141
                                                                      11. Kaufman A, Kramer M, Godmere RO. Hemodialysis access
Acknowledgements. The authors would like to thank the patients            recirculation (R) measured by blood temperature monitoring
participating in this study, and the Fresenius company for supply
                                                                          (BTM): a new technique [abstract]. J Am Soc Nephrol 1991;
of blood thermodilution monitor (BTM) during the trial period.
                                                                          2: 232.
                                                                      12. Sands J, Glidden D, Jacavage W, Jones B. Difference between
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                                                                      Received for publication: 4.3.02
                                                                      Accepted in revised form: 6.1.03