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

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1 Nephrol Dial Transplant (2003) 18: DOI: /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 Background. A method is presented for estimating the confidence limits (CLs), or accuracy, of the arteriovenous fistula flow rate measured at haemodialysis by the on-line thermodilution technique. Methods. This was by derivation of an expression to estimate what variance a set of repeated measures of flow would yield, using values pertaining to a single measure of flow. (Laws of variance were applied to the formula used to calculate flow, to account for its variables values and measurement errors.) This enabled CLs of a single measure to be estimated. Results. The variance estimated from a single measure was compared with that actually observed upon immediately taking a second measurement; differences in 189 pairs were not significantly different from zero (Ps0.56). Applying the results demonstrated that measured flow values of mlumin typically had associated 95% CLs that included 500 mlumin; therefore, true flow could not be said to be either side of 500 mlumin. The same was the case for mlumin with regard to 600 mlumin. CLs widened considerably with the magnitude of flow rate, limiting the accurate measurement of higher flows and the detection of falls in flow. Conclusion. A method to estimate CLs of flow rate measured by the thermodilution technique is presented and validated. Application demonstrates an accurate measurement of low flow, but limitations at higher flow and in detecting falls in flow. Appreciating the magnitude of such is critical to informed clinical decision making when using flow rate in an access surveillance programme. Keywords: access flow; accuracy; haemodialysis; thermodilution; vascular access Correspondence and offprint requests to: Dr J. L. Ragg, 26 Learmonth Street, Ballarat, Victoria 3350, Australia. joe.ragg@mh.org.au Introduction Major consensus guidelines have recommended the measurement of the flow of arteriovenous fistulae as the preferred means of monitoring their function, along with physical examination [1,2]. Specifically, investigation of fistulae is recommended where flow rate is below a particular threshold (500 and 600 mlumin in native and graft arteriovenous fistulae, respectively), or where there is a fall in flow rate (20 25% or more from baseline in either of these fistulae). There is expectation that on-line techniques of measuring flow rate will supplant others in enabling accurate and inexpensive repetitive measurements [1]. A number of reports have validated flow rates measured by such methods [3 9], and others have identified factors that will compromise its accuracy [4]. However, no study has aimed solely to describe confidence limits (CLs) of measured flow, which are an easily understood and clinically applicable expression of measurement accuracy. Knowledge of the accuracy of on-line flow measurements is of clinical significance, as intervention is recommended based on the value of these measurements. The aims of this study were to describe a method to estimate the CL of access flow rate as measured by the on-line thermodilution technique, and to apply this to clinical decision making when assessing arteriovenous fistulae and grafts. Subjects and methods Patients participating were all those attending a satellite dialysis centre of a teaching hospital for stable chronic haemodialysis patients. Flow measurement technique Flow rate (Q) was measured by the on-line thermodilution technique, as described and validated by Schneditz et al. [8]. This requires the substitution of the equation given for cardiopulmonary recirculation (Equation 6 in Schneditz et al. # 2003 European Renal Association European Dialysis and Transplant Association

2 956 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 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 (Rn 1{Rx Rx(1{ ð ÞðQx{UFRÞ) ðrxð1{rnþqnþ transformations approximated the normal (kurtosis near to 3, and skewness near to 0). Secondly, SDs of the distributions were not constant (they increased with the median flow rate of the Q distribution, or vice versa for their inverse transformations). Figure 1 illustrates the distributions obtained relevant to the patient with a flow rate lying on the 50th percentile of all observed. where Rn and Rx are the recirculation of dialysis lines in the usual and transposed positions, respectively; Qn and Qx are the extracorporeal blood flow rate, concurrent with the above Rn and Rx readings, respectively; and UFR is the ultrafiltration rate (constant throughout the whole flow measurement). The technique is invalid where there is recirculation in the fistula. Therefore, where Rn values were )15% [10], measurements were excluded from analysis. Nonsensical readings (arbitrarily those )6.5 lumin or negative flows) were also excluded. These arise from very low recirculation measures with lines in the transposed position, raising the possibility that the venous needle is not directly downstream of the arterial needle, e.g. in a collateral vein coming off upstream of the arterial needle or in a separate vein all together. Pairs of flow readings were taken, as per the following approach. In the first hour of dialysis, a pair of Rn readings was recorded, along with the concurrent Qn (as per machine digital display). Lines were transposed and, similarly, a pair of Rx and the concurrent Qx were recorded. The UFR (as per machine digital display), constant throughout all measurements, was recorded. Two flow rates were calculated according to Equation 1, using the first value in each pair, and then the second, along with the constant UFR. This was an approximation to taking two immediately sequential flow readings (i.e. the need to transpose lines repeatedly, thereby subjecting the patient to a small but theoretical risk of crossinfection was avoided). All measurements were performed using Fresenius 4008B dialysis machines fitted with a blood thermodilution monitor (BTM). Arterial needles faced the anastomoses and were as near to it as possible. Vascular access was obtained with 14- gauge arterial and venous needles and Fresenius blood lines. Measurement error of recirculation and extracorporeal blood flow rate Recirculation as measured by the BTM has been validated elsewhere [11]. In this study, measurement accuracy of recirculation was assumed to be reflected by the immediate reproducibility of the measure, and this was quantified by considering the SDs of small sets (pairs) of recirculation 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 of all SDs calculated. For the purposes of this study, a measurement error of 4% coefficient of variation for extracorporeal blood flow rate was assumed (see Discussion) [12], and this was assumed to be unaffected by access flow rate. Estimation of the confidence limits of measured flow rate The 95% CLs of a single flow (Q) measure can be calculated as being 1.96 standard measurement errors either side of a single measure, assuming that the distribution of repeated measures is normal in nature. Table 1 demonstrates that such a distribution is not normal in nature (see above), but that the inverse transformation, invq, with a corresponding SD of SD invq reasonably approximates normal (kurtosis near to 3, and skewness near to 0). The CLs calculated instead for invq are valid. CLs on the scale of Q can then be calculated by: 1 95% CLs for Q~ ð2þ ½invQ+1:96 SD invqš As is also demonstrated in Table 1, SD invq is not constant. Specifically, it decreases with increasing magnitude of flow rate. Therefore, an expression is required for substitution into Equation 2. The variance of the general function y, of the random variables x1, x2, x3... whose variances are known, and where each x is independent of the other, can be approximated by varðyþ~ ½y ðx1þš 2 varðx1þz½y ðx2þš 2 ð3þ varðx2þz½y ðx3þš 2 varðx3þšz... 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. Analogously, the function invq is of the variables Rn, Rx, Qn and Qx whose variances (measurement error) are known, each of which is independent of the others. Values can be substituted accordingly to yield an expression for the variance of the invq function (and therefore its standard deviation, SD invq). A qualification is that the expression is not calculated at the mean or true values of each variable (see Appendix). For simplicity, the measurement error of UFR is not discussed, Table 1. Summary of the distributions representing repeated measures of flow rate (computer simulation) for those patients whose flow rate lay on the 10th, 30th, 50th, 70th and 90th percentiles of all those measured (with the inverse transformation also shown) Percentile Q (mlumin) SD Skewness Kurtosis Computer simulation of repeated measures of flow rate A computer simulation of repeating flow measurements times, in those patients whose fistula flow rate lay on the 10th, 30th, 50th, 70th and 90th percentiles of those measured, was undertaken. This was by noting the value of the variables used to calculate flow at the particular percentile, and generating sets of such variable values (the mean being the originally noted value, with spread equal to that 10th th th th th th Inv th Inv th Inv th Inv th Inv

3 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 measurements. Finally, the measurement error of recirculation can be lessened by taking two immediately sequential measures and averaging these (lessened to a new value of measurement error ud2, the standard error of a mean of two values). Herein, CLs for flow rate, where flow rate is calculated using such values, are referred to as CL2, whereas in the instance of using just single measures of recirculation, they will be referred to as CL1. Ethics Ethical approval was granted by the Top End Human Research Ethics Committee. Statistical analysis Values were expressed as median (IQR, interquartile range). Correlation of continuous variables was tested by Kendall s rank correlation coefficient (T). The null hypothesis that 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 P Results There were 56 patients studied (and 56 fistulae). They were of age 51 years (IQR 46 59) and 35 were female. All fistulae were native, although two were interposition 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 ), Rx 25.4% (IQR ), Qn 275 mlumin (IQR ), Qx 248 mlumin (IQR ) and UFR 760 mluh (IQR ), and the calculated flow was 919 mlumin (IQR ). Correlation of repeated flow measures There was good correlation between repeated measures of flow rate (Ts0.68, P-0.001) although the repeatability lessened considerably with increasing magnitude of flow rate. This is illustrated in Figure 2. Measurement error of recirculation and extracorporeal blood flow rate The magnitude of difference within Rn pairs was not related to its averaged value (Ts0.03, Ps0.55). It was related for Rx pairs (Ts0.14, Ps0.006), but to a relatively small real extent only (Table 2). The median SD of all Rn pairs was 1.48, and of all Rx pairs was Confidence limit of a measured flow rate Equation 3 estimates the variance that repeated measures of invq would have by using variables pertaining to a single measure of flow. This is to enable the calculation of confidence limits of a single measure of flow according to Equation 2. To test this, variables and their measurement error relevant to the calculation of the first Q in each of the 189 pairs were substituted. Fig. 2. Correlation of immediately sequential flow measurements.

4 958 J. L. Ragg et al. Table 2. The standard deviation of a pair of Rx measurements Average n Median SD ) 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 a CLs estimated according to Equation 2, where either single measures of Rn and Rx (CL1), or two measures each of Rn and Rx were taken and averaged (CL2), before substitution to calculate the access flow rate by Equation 1. The differences between the variance estimated by Equation 3 and that actually observed in all 189 pairs were not significantly different from zero (Ps0.56). Examples of practical application There was considerable widening of CLs of the measured access flow rate, or a lesser reproducibility of measurement, with increasing access flow rate. This is demonstrated in Table 3, which gives flow rates lying on various percentiles of all those measured, along with their estimated CL1 and CL2 values. This is also demonstrated in Figure 2, which shows graphically the immediate reproducibility of access flow rate measurements, and Figure 3 which demonstrates graphically all flow rate measurements with estimated CL2 values. The observed flow rates with estimated upper or lower CLs (CL2) nearest 500 mlumin were 427 mlumin ( ) and 559 mlumin ( ), respectively, which indicates that a measured flow rate of ; mlumin will indeterminately classify the true access flow rate to be either side of a 500 mlumin threshold. Similarly, for a 600 mlumin threshold, flow rates with estimated CL2 limits of 529 mlumin ( ) and 709 mlumin ( ) indicate that a measured flow rate of ; mlumin will indeterminately classify the true flow rate to be either side of a 600 mlumin threshold. Very large falls in measured flow rate need to occur to determine a true 20% fall in flow rate, particularly falls from the higher flow rates. Table 4 gives arbitrary Q Fig. 3. Observed flow rates up to 2500 mlumin, and their estimated CL2 limits. Table 4. Flow rate example (Q) and values 20% less, and the flow rates whose estimated CL2 values lay immediately next to these values Q (CL2) Q Q less 20% Q (CL2) 696 ( ) ( ) 1093 ( ) ( ) 1621 ( ) ( ) 1955 ( ) ( ) 2591 ( ) ( ) values, and their values minus 20%, with the measured flow rates whose estimated upper or lower CL2 limits 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 indicate a true 20% fall in flow rate. Discussion The main findings from this study were the increasing width of the CLs with higher flow rates, as shown in Table 3, consistent with there being a much lesser repeatability of measure in patients with higher fistula flow rates, as shown in Figure 2. As demonstrated, it is both the value of, and the measurement error of, the component variables of the equation to calculate flow rate, along with the mathematical properties of the equation used to calculate flow rate, that ultimately determine the measurement error or repeatability of the calculated flow rate. Whilst measurement errors of the component variables of the equation to calculate flow rate are constant across access flow rates, measurement error of the calculated flow rates is not. It increases with access flow rate in a somewhat exponential fashion. It is this, rather than a physiological phenomenon, that explains the increasing measurement error of calculated access flow rate with access flow rate by the thermodilution technique. Such a pattern has been noted previously, but not quantified;

5 CL limits of AV fistula flow rate measured by on-line thermodilution Schneditz et al. [8] noted that paired readings obtained by the on-line thermodilution method had good correlation only to flows of 1.5 lumin. Also of note is the eccentric placement of the CLs about the Q value. This is consistent with the skew distribution that results from repeated measures of Q, as demonstrated in Table 1 and Figure 1. There is some consensus that the optimal access flow rate thresholds indicating impending native and graft fistulae dysfunction are 500 and 600 mlumin, respectively [2]. This study indicates that measured flow rates of mlumin and mlumin indeterminately classify access flow rate either side of these thresholds. Therefore, to justify fistulae intervention upon obtaining flow measures within these ranges, even greater importance needs to be placed on corroborating clinical and surveillance method evidence of impending fistula dysfunction. There is consensus that a fall in access flow rate of 20 25% or more is indicative of impending fistula dysfunction [2]. For practical purposes, this study indicates that the thermodilution technique of measuring access flow rate has limited sensitivity in detecting such falls, particularly as mentioned in the Results, from the higher access flow rates. While flow measurement increasingly is recommended as the preferred method of surveillance of arteriovenous fistulae function, there is limited literature pertaining to the measurement error of recirculation, extracorporeal blood flow rate and fistula flow rate measured by the thermodilution technique and, to some extent, by other methods. Regarding recirculation by the thermodilution technique, Schneditz et al. [9] have expressed reproducibility as the difference between paired readings. This was 0.4"1.84% (ns52) for Rn readings and 0.29" 3.26% (ns54) for Rx readings. Our values, calculated by the same method, were less reproducible at 0.00" 3.26% and 0.00"3.46%, respectively. Wang et al. [10] expressed the reproducibility as the relative deviation from the mean of two consecutive measures, (R1 R2) 3100u(mean of R1 and R2), and for Rn and Rx readings combined this was 2.5"11.5% (ns220). Our value, calculated in the same way, was less reproducible at 1.1"33.3%. Another independent dialysis unit reported a similar measurement error using a similar machine and BTM monitor: a median SD of 1.63 (ns97) and 1.34 (ns97) for Rn and Rx pairs of readings, respectively (D. Bolsch, Hartley Dialysis Center Adelaide, Australia, personal communication). Relevant to the ultrasound dilution technique of measuring recirculation, Depner et al. [14] described the reproducibility of Rx measures by the Pearson correlation coefficient and the mean absolute error of paired readings as 0.98, 3.9"2.8%, which was similar to that calculated for this study (0.92, 2.6"2.4). Regarding the measurement error of extracorporeal blood flow rate, the Fresenius 4008B machine gives a digital readout of Qn and Qx. Displayed extracorporeal blood flow rates have been shown not to be perfectly accurate. There is limited literature pertaining exclusively to the Fresenius machines. Sands et al. [12] compared extracorporeal flow rate displayed on the Fresenius 2008H machine with readings obtained by an on-line sensor of extracorporeal blood flow (Transonic 2 haemodialysis monitor). The flow rate displayed slightly overestimated flow in comparison with the on-line sensor, with a measurement error coefficient of variation of ;5 6%. The measurement error may have been overestimated, as there must be at least some measurement error associated with the Transonic 2 haemodialysis monitor against which it was compared. Furthermore, intra-patient measurement errors were not reported. Conceivably, these could be less than the values reported, which were for all patients measures combined. The reproducibility of flow measurement by the thermodilution technique has been expressed by Schneditz et al. [9] as the mean difference between pairs of readings. This was 26"298 mlumin (ns52). However, this summary statistic does not account specifically for the lesser reproducibility at higher flow rates. Nor was it clear if in the calculation of flow, the recirculation measures were a single measure or the average of a pair. In the same paper, flow rate estimated by the ultrasound dilution technique gave a slightly better reproducibility of 27"212 mlumin. Our value, calculated in the same way, using single recirculation measurements to calculate flow was less reproducible at 10"453 mlumin. Also of relevance to the ultrasound dilution technique, an in vivo validation [3] expressed reproducibility of flow rate as the coefficient of variation (SDumean) of 46 sets of five consecutive measures, and this was 13.4"6.4%. There was no significant difference across three brackets of flow magnitude. In this study, with single measures of variables to calculate flow rate, this was less at 16.2"14.6%. As expected, the reproducibility was better at lower flow rates. Across three equal centile brackets of flow rate, these were 12.2"9.9, 16.1"11.6 and 20.0"19.1%. This would suggest that the accuracy of measurement by the thermodilution technique is comparable with that by the ultrasound dilution technique. This is so particularly at the more critical lower flow rates, and where two recirculation measures are taken and averaged before entering into the equation to calculate flow rate (see the improvement in CL2 over CL1 (Table 3). Conclusion 959 This study presents and validates a method to estimate confidence limits of flow rate measured by the thermodilution technique. Application demonstrates reasonably accurate measurement of low flow, but limitations at higher flow and in detecting falls in flow, and awareness of this is critical to informed clinical decision making where using flow rate in access surveillance programmes.

6 960 J. L. Ragg et al. Appendix The true mean or true value of each of the variables used to calculate flow are not known, and therefore conditions for applying Equation 3 are not fully met. The effect on the accuracy of the calculated CLs was investigated as follows. The true flow rate should in 95% of instances be contained within the 95% CLs. Consider again the aforementioned computer simulation, of taking consecutive flow rates in the patients whose flow rate lay at the 10th, 30th, 50th, 70th and 90th percentiles of all flow rates measured. A random sample of 1000 from each was taken. The CL for each of these flow rates was calculated according to Equation 2. The true flow rate (median flow rate of the overall distribution) was outside the relevant CL in 202 of the 5000 (4.0%) instances. This would validate the calculation of the CLs according to Equations 2 and 3 as being reasonable despite the conditions for applying Equation 3 not being fully met. Acknowledgements. The authors would like to thank the patients participating in this study, and the Fresenius company for supply of blood thermodilution monitor (BTM) during the trial period. References 1. National Kidney Foundation. KuDOQI Clinical Practice Guidelines for Vascular Access, Am J Kidney Dis 2001; 37: S137 S Ethier JH, Lindsay RM, Barre PE et al. Clinical practice guidelines for vascular access. Canadian Society of Nephrology. J Am Soc Nephrol 1999; 10 [Suppl 13]: S297 S 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: Krivitski NM. Theory and validation of access flow measurement by dilution technique during hemodialysis. Kidney Int 1995; 48: Lindsay RM, Blake PG, Malek P et al. Hemodialysis access blood flow rates can be measured by a differential conductivity technique and are predictive of access clotting. Am J Kidney Dis 1997; 30: Lindsay RM, Bradfield E, Rothera C et al. A comparison of methods for the measurement of hemodialysis access recirculation and access blood flow rate. ASAIO J 1998; 44: Lindsay RM, Blake PG, Malek P et al. Accuracy and precision of access recirculation measurements by the hemodynamic recirculation monitor. Am J Kidney Dis 1998; 31: Schneditz D, Fan Z, Kaufman A, Levin NW. Measurement of access flow during hemodialysis using the constant infusion approach. ASAIO J 1998; 44: Schneditz D, Wang E, Levin NW. Validation of haemodialysis recirculation and access blood flow measured by thermodilution. Nephrol Dial Transplant 1999; 14: Wang E, Schneditz D, Kaufman AM, Levin NW. Sensitivity and specificity of the thermodilution technique in detection of access recirculation. Nephron 2000; 85: Kaufman A, Kramer M, Godmere RO. Hemodialysis access recirculation (R) measured by blood temperature monitoring (BTM): a new technique [abstract]. J Am Soc Nephrol 1991; 2: Sands J, Glidden D, Jacavage W, Jones B. Difference between delivered and prescribed blood flow in hemodialysis. ASAIO J 1996; 42: M717 M Armitage P, Berry G. Statistical Methods in Medical Research. Blackwell Science, Oxford, UK, 1994: Depner TA, Krivitski NM, MacGibbon D. Hemodialysis access recirculation measured by ultrasound dilution. ASAIO J 1995; 41: M749 M753 Received for publication: Accepted in revised form: