Kidney International, Vol. 60 (2001), pp. 284–291

DIALYSIS – TRANSPLANTATION

Noninvasive transcutaneous determination of accessblood flow rate

ROBERT R. STEUER, DAVID R. MILLER, SONGBIAO ZHANG, DAVID A. BELL,and JOHN K. LEYPOLDT

In-Line Diagnostics Corporation, Kaysville; Research Service, VA Medical Center, and Departments of Internal Medicine andBioengineering, University of Utah, Salt Lake City, Utah, USA

Conclusions. These results show that transcutaneous mea-Noninvasive transcutaneous determination of access blood flowsurement of Qa is an accurate, simple, and fast technique forrate.determining Qa without requiring the reversal of the dialysisBackground. Current indicator dilution techniques for de-blood lines.termining the vascular access blood flow rate (Qa) require re-

versal of the dialysis blood lines and are time consuming. Wehave recently described an indicator dilution technique fordetermining Qa using a novel optical transcutaneous hematocrit Routine determination of the rate of blood flow within(Hct) sensor that does not require reversal of the dialysis lines,

the vascular access during maintenance hemodialysis isand have validated the accuracy of this method (TQa) in vitro.currently considered an integral component of vascularMethods. This study compared results using the TQa method

with those obtained using a similar indicator dilution technique access assessment [1]. Although the relative importancebut which required reversal of the dialysis lines (HD01 Moni- of vascular access flow rate and venous pressure mea-tor, Transonic Systems, Ithaca, NY, USA) during routine he- surements [2, 3] in detecting venous stenoses is still con-modialysis in 59 patients (25 native fistulas and 34 synthetic

troversial [4–6], both the magnitude [5, 7–13] and thegrafts). The sensor for the TQa method was placed on the skinrate of decrease [14] in the vascular access flow rate havedirectly over the access to measure changes in Hct approxi-

mately 25 mm downstream of the venous needle. A single 30 been shown to predict venous thrombosis and accessmL bolus of saline was infused into the dialyzer venous line failure. The traditional approach for determining theover approximately six seconds without reversal of the dialysis vascular access flow rate is by Doppler flow imaging [15];blood lines, and the vascular access flow rate was calculated

however, these procedures are expensive and cannot beusing indicator dilution methods from the time-dependent de-performed during routine hemodialysis. Furthermore,crease in the Hct downstream of the venous needle. Two addi-

tional small-scale studies were performed to assess the effect the results using this approach are dependent on theskin pigmentation and to evaluate further the reproducibility machine [16] and operator.of the TQa method. The vascular access flow rate can also be accurately

Results. Qa values determined by the TQa method weredetermined using indicator dilution methods. Early indi-highly correlated with those determined by the HD01 methodcator dilution studies measured the vascular access flow(N � 72, R2 � 0.948, P � 0.001) over the range of 153 to 2,042rate by injecting cardiogreen [17] or radiolabeled [18–20]mL/min. There was no significant difference between vascular

access flow rates determined by the TQa method and those substances at a constant rate into the arterial end of thedetermined by the HD01 method. Results from one small- access, and calculated the vascular access flow rate fromscale study showed that the relationship between Qa values the steady-state downstream concentration of the in-determined by the TQa and the HD01 methods was similar

jected substance. These early attempts to use indicatorwhen tested only among black patients (N � 12), suggestingdilution methods were limited to research applicationsthat skin pigmentation is not an important determinant of the

accuracy of the TQa method. The second small-scale study since this approach could not be routinely performedshowed that the intratreatment coefficient of variation for the during clinical hemodialysis. To determine the vascularTQa method was 7.8 � 5.6% (N � 14). access flow rate during the hemodialysis procedure, Kriv-

itski and Depner showed how reversal of the dialysisblood lines (switching the arterial and venous connec-Key words: hematocrit, indicator dilution, vascular access, Qa, dialysis,

maintenance hemodialysis, optical Hct scanner. tions) would direct the blood flow within the hemodialy-sis circuit to facilitate the injection of an indicator in theReceived for publication August 2, 2000arterial end of the access and its detection downstreamand in revised form December 14, 2000

Accepted for publication January 19, 2001 [21–23]. Various modifications of this approach subse-quently have been developed [8, 24–27]. While these 2001 by the International Society of Nephrology

284

Steuer et al: Transcutaneous determination of access flow 285

Fig. 1. Cross-sectional illustration of the photo-optical sensor used in the transcutaneous bloodflow rate (TQa) method. A light-emitting diode(LED) and photodiode (or photodetector)components of the transcutaneous Hct sensorplaced on the skin directly over the access.The volume of tissue illuminated by the LEDillustrates the reflective penetration of thephotons (�) as seen by the photodetectors inthe process of determination of the Hct, whichincorporates the access site and the photonpropagation in the tissue volume not con-taining the access (�0). Details are in the text.

indicator dilution methods permit determination of the are mathematically expressed in terms of a bulk attenua-tion coefficient (�), which is specific to the illuminatedvascular access flow rate during routine hemodialysis,

reversal of the dialysis blood lines from their normal media. The amount of light detected by the photodetec-tor is proportional via a modified Beer’s law formula toconfiguration is inconvenient and time consuming, since

it requires that the dialyzer blood pump be stopped and the instantaneous net � value of the media [28]. Themathematical details describing the relationship betweenthe dialysis lines disconnected. Furthermore, some of

these indicator dilution methods also require accurate the intensity of light detected by the photodetector andthe Hct are shown in Appendix 1.determination of the dialyzer blood flow rate.

We have developed an optical hematocrit (Hct) sensor When the volume of tissue illuminated includes all oreven part of the access, the resultant � value includesthat can detect changes in Hct transcutaneously and have

shown how such a sensor could be used to determine the information about both the surrounding tissue and theaccess itself. In order to resolve the signal due to bloodvascular access flow rate without reversal of the dialysis

blood lines in an in vitro model hemodialysis circuit flowing within the access from that due to the surroundingtissues, the sensor system illuminates adjacent tissue re-(abstract; Steuer et al, J Am Soc Nephrol 11:198A, 2000).

Our current study evaluated the accuracy and variability gions on either side of the access (Fig. 1). Values of �0

for tissue regions not containing the access are then usedof this new approach for determining the vascular accessto normalize the signal, thus providing a baseline fromflow rate during routine hemodialysis.which relative changes in access Hct can be assessed.

METHODS Indicator dilution methodSensor description Figure 2 illustrates blood flow through a hemodialysis

vascular access with the dialysis blood lines in the normalThe optical sensor system consists of a light-emittingconfiguration and the key features of the current (TQa)source (an LED of specific wavelength) and a comple-method. The transcutaneous Hct sensor is placed directlymentary photodetector. In this application, a wavelengthover the vascular access downstream of the venous dial-of 880 nm was used because it is near the known isobesticysis needle. The sensor and associated monitoring systemwavelength for hemoglobin, is commercially available,continuously records a signal proportional to the Hctand has been shown to be effective in the optical determi-from which the relative change in Hct in the vascularnation of whole blood parameters such as Hct and oxy-access can be accurately determined (Appendix 1). Aftergen saturation [28].a stable baseline value (proportional to the Hct in theWhen the sensor is placed on the surface of the skin,access or Ha) is obtained, a known volume (V) of normalthe LED illuminates a volume of tissue, and a smallsaline is injected via a syringe into the dialysis venousfraction of the light absorbed and backscattered by theline that reduces the Hct beneath the sensor H(t) duringmedia is detected by the photodetector, as shown inand immediately following the injection. The vascularthe cross-sectional diagram of Figure 1 [29]. While lightaccess flow rate (Qa) can be calculated using bolus injec-travels in a straight line, the illuminated volume as seention, indicator dilution principles [30] from the followingby the photodetector may be visualized as an isointensityequation (Appendix 2):ellipsoid, as individual photons of light are continuously

scattered and absorbed by the media (Fig. 1). Since aQa � V/��H(t)/Hadt (Eq. 1)

wavelength of 880 nm was chosen, hemoglobin of theblood within the tissue volume is the principal absorbing where �H(t) denotes Ha � H(t), and the integral (area

under the curve) in this equation is from the time ofsubstance. The scattering and absorbing characteristics

Steuer et al: Transcutaneous determination of access flow286

configuration, and the dialyzer blood pump was re-started. The transcutaneous Hct sensor was placed onthe skin over the patient’s vascular access approximately25 mm downstream of the venous needle. Thirty milli-liters of normal saline solution were then injected intothe venous needle at a rate of approximately 300 mL/min to determine vascular access blood flow rate by theTQa method. In six patients, saline was injected directlyinto the arterial dialysis needle before connecting theneedle to the complete dialysis circuit. In two patients,saline was injected directly into the access by using aneedle and syringe. The data from these various methodswere combined together, independent of where salinewas injected into the access. In 38 patients, this measure-ment was performed in duplicate to assess the replicabil-ity of this method.

Two additional small-scale studies were performed toassess the effect of skin pigmentation and to evaluate

Fig. 2. Schematic diagram of the hemodialysis circuit. The injection the reproducibility of the TQa method further. In one of(syringe) and measurement sites (TQa � Hct sensor) are indicated. The these studies, 12 additional black patients were evaluatedHcts and flow rates under steady-state conditions are also indicated.

using the protocol described previously in this article,Abbreviations are: Qa, access flow rate; Qb, dialyzer blood flow rat; Qi,injection flow rate; Ha, Hct in the access flow; Ho, Hct at the sensor. and vascular access flow rates determined by the TQa

and HD01 methods were compared. In the second small-scale study, the vascular access blood flow rate was deter-mined twice in 14 patients during the same hemodialysis

injection (t � 0) to where the signal has returned to the session after the sensor had been removed and reposi-baseline value (t � ∞). This equation is valid independent tioned on the skin surface. In both of these latter studies,of the rate of saline injection or the dialyzer blood flow the saline bolus was always injected into the arterialrate. dialysis needle when determining vascular access flow

rate by the TQa method.In vivo studies

The 59 patients initially studied were recruited from Statisticsfour different dialysis units (Bonneville Dialysis Unit, All measured and calculated values are reported asOgden, UT, USA; Taylorsville Dialysis Unit, Taylorsville, mean � SD. The significance of differences in calculatedUT, USA; Central Valley Dialysis Unit, Salt Lake City, vascular access flow rates by the TQa method and thoseUT, USA; and Southeastern Wyoming Dialysis Center, by the HD01 method was determined using a pairedCheyenne, WY, USA). Prior to the study dialysis session, Student t test. The variability of the slope and intercepta disposable tubing with an injection port (CO-daptoR; from the regression equation is expressed as � the esti-Transonic Systems, Ithaca, NY, USA) was placed be- mated SD (or the estimated SE). The results from thetween the venous dialysis tubing and the venous needle. replicability and reproducibility studies are expressed asThe dialysis circuit was primed with saline in the usual the mean � SD coefficient of variation for the duplicatefashion taking extra care to remove any air bubbles from measurements. P values of less than 0.05 were consideredthe venous injection port. statistically significant.

Within the first hour of dialysis, access recirculationwas first measured by the HD01 monitor (Transonic Sys-

RESULTStems). Then the dialyzer blood pump was stopped. Thedialysis lines were reversed from their normal configura- The characteristics of the patients initially studied aretion, and the vascular access flow rate was determined shown in Table 1, and the characteristics of the accessesin duplicate by the HD01 method. During these tests, studied are shown in Table 2 (N � 59). The patientsinjection of saline was performed using the saline release studied were predominantly male and white. Althoughmethod (abstract; Krivitski et al, J Am Soc Nephrol 8: the distribution of race in our study is not representative164A, 1997). The dialyzer blood pump was again stopped, of that within the United States as a whole, it is represen-and the dialysis lines were returned to their normal con- tative of the population in this geographic region. Thefiguration. age of the patients, the fraction of diabetic patients, and

the fraction of patients with synthetic polytetrafluoro-After dialysis, blood lines were returned to the normal

Steuer et al: Transcutaneous determination of access flow 287

Table 2. Access characteristics (N � 59)Table 1. Patient characteristics (N � 59)

Characteristic Value Characteristic Frequency

PTFE grafts 34/59 (57.6%)Age years 65�15Male 42/59 (71.2%) Access location

Upper arm 22/59 (37.3%)Diabetic 28/59 (47.5%)Race Lower arm 35/59 (59.3%)

Leg 2/59 (3.3%)White 42/59 (71.2%)Black 5/59 (8.5%) PTFE is polytetrafluoroethylene.American Indian 1/59 (1.7%)Asian 1/59 (1.7%)Hispanic 10/59 (16.9%)

Data are frequency or mean � SD.in a separate group of 12 additional black patients [3native arteriovenous (AV) fistulas and 9 PTFE grafts].There was no significant difference between vascularaccess flow rates determined by the TQa method (861 �ethylene (PTFE) grafts were similar to those for chronic

hemodialysis patients in the United States. Eleven of 164 mL/min) and those determined by the HD01 method(830 � 218 mL/min), and the best fit linear-regressionthese patients were studied twice, and one patient was

studied three times; all other patients were studied once line of these data also had a slope not different fromunity and a small y intercept. The equation of this linefor a total of 72 measurements. Access recirculation was

significant in three patients. In these patients, the blood was Y � 1.16 (�0.21) � X � 169 (�180) mL/min, R2 �0.761. The absolute difference in measured vascular ac-pump setting was reduced to 150 mL/min to eliminate

access recirculation before completing the study protocol. cess flow rates between the TQa and HD01 methods inthis study was 92 � 62 mL/min. To compare these resultsFigure 3 shows an example plot of the function de-

scribed in Appendix 1 that is proportional to the time with those in the initial study, the data are also plottedrate of change of Hct and is measured by the sensor when in Figure 5. No systematic differences in the results fromusing the TQa method. Since the function is dependent on these two studies are obvious.the time rate of change in Hct, its value is steady at zero The coefficient of variation described previously in thisuntil the injection of saline has begun. Approximately article may not accurately reflect the true reproducibilityfive seconds after the injection, the value of this function of the TQa method, since the sensor remained in the sameincreases and then decreases after a time period propor- position on the skin during both measurements. An addi-tional to the length of the injection. This measured func- tional small-scale study was therefore performed in 14tion was then integrated over the length of the injection to patients (11 white and 3 black; 2 native AV fistula anddetermine the vascular access flow rate using Equation 1. 12 PTFE grafts) to determine the true reproducibility of

Figure 4 shows values of the vascular access flow rate the TQa method after the sensor had been removed fromdetermined by the TQa method plotted versus those de- and repositioned on the skin. The results from this studytermined by the HD01 method in this initial patient showed that the first vascular access blood flow rategroup. The best fit linear-regression line had a slope of measurement (545 � 245 mL/min) was not different fromessentially unity and a small y intercept, and there was the second (552 � 242 mL/min). The intratreatment co-no significant difference between vascular access flow efficient of variation for this evaluation was 7.8 � 5.6%.rates determined by the TQa method and those deter-mined by the HD01 method. Figure 5 shows these same

DISCUSSIONresults plotted using an alternative approach to assessIn order to use indicator dilution techniques to mea-the agreement between two methods of clinical measure-

sure the vascular access flow rate during hemodialysis,ment [31]. The agreement between these methods wasthe indicator must be injected upstream and its concen-excellent; the absolute difference in measured vasculartration detected downstream in the blood flowing throughaccess flow rates between the TQa and HD01 methodsthe vascular access. Reversing the dialysis blood lineswas 71 � 62 mL/min. When these results were furtherduring the hemodialysis treatment permits applicationanalyzed for various patient subgroups (male vs. female,of indicator dilution principles by direct injection of thediabetic vs. nondiabetic, synthetic grafts vs. native fistu-indicator into the venous dialysis tubing. However, thelas), excellent agreement between the measured flowapproach described in this study (TQa method) permitsrates was similarly observed. The mean intratreatmenta unique application of indicator dilution principles, sincecoefficient of variation for the TQa method was 10.5 �the sensor can detect a dilution signal downstream of the6.8%, and that for the HD01 method was 8.9 � 9.5%;venous needle through the skin. This geometry permitsthese differences were not statistically significant.determination of the vascular access flow rate withoutThe number of black patients in the previously men-

tioned study was small; thus, this protocol was repeated reversal of the dialysis blood lines, thereby maintaining

Steuer et al: Transcutaneous determination of access flow288

Fig. 3. Function F(i, di/dt) measured by thetranscutaneous sensor plotted as a function oftime during one experiment. The area underthis curve is computed to calculate the vascu-lar access flow rate using Equation 1.

Fig. 4. Vascular access flow rates (Qa) deter-mined by the TQa method compared withthose determined by the saline dilution method(HD01 monitor; Transonics). The line indi-cated is that obtained by best fit linear regres-sion. The equation of this line is Y � 0.953(�0.27) � X � 36 (�22) mL/min.

optimal dialysis efficiency throughout the entire treat- nephrologists because it is also possible to determinethe vascular access flow rate when the patient is in thement.

The current approach is related to several previous physician’s office or in the clinic, instead of during hemo-dialysis, by injecting saline solution directly into the ac-attempts to determine the vascular access flow rate by

injecting various indicators at a constant rate into the cess and measuring changes in transcutaneous Hct withthe optical sensor. During the initial study, eight patientsarterial end of the access to calculate the vascular access

flow rate from the steady-state downstream indicator con- had vascular access flow rate determinations by directinjection of saline into the access prior to dialysis; theircentration [17–20]. These early approaches were limited

to the constant infusion indicator dilution approach as results were later confirmed once the dialysis circuit wasin place. Furthermore, the two additional studies werethe indicator concentration was measured in discrete

blood samples (Stewart Principle [30]). The TQa method also performed exclusively with this alternative methodfor injecting saline into the access with excellent results.described herein permits the use of the bolus injection,

indicator dilution approach since the described optical Thus, it may now be possible to monitor the vascularaccess flow rate regularly as an indicator of access func-sensor can accurately determine instantaneous changes

in Hct (Henriques-Hamilton-Bergner Principle [30]). This tion when the patient is not being dialyzed as well asduring maturation of native fistulas prior to first use.optical approach is likely to be of considerable interest to

Steuer et al: Transcutaneous determination of access flow 289

Fig. 5. Access blood flow rates (Qa) deter-mined by the TQa method compared withthose determined by the saline dilution method(HD01 monitor; Transonics) using a Bland-Altman plot [31]. Symbols are: (�) resultsfrom the initial study; (�) results from theadditional study of only black patients.

The accuracy of the TQa method depends critically on nature of these measurements suggests that the sensitiv-at least two factors. As can be seen in Equation 1, the ity of the calculated vascular access flow rate to skincalculated vascular access flow rate depends directly on melanin content is minimal. Our observations on blackthe volume of saline injected; therefore, care must be patients suggest that skin pigmentation is not a majortaken to inject a given amount of saline over a specified concern.time interval. The time interval for injection does not We conclude that transcutaneous measurement of Qa

need to be known precisely; however, it is important is an accurate, simple, and fast technique for determiningthat it be less than approximately 10 seconds to avoid Qa without reversal of the dialysis blood lines. Furthersignificant interference caused by cardiopulmonary recir- studies to determine the potential importance of otherculation of the injected saline solution. The second factor clinical parameters (such as patient obesity and collateralthat is important to consider in the accuracy of the TQa circulation in fistulas) on the accuracy of this methodmethod is the placement of the sensor to determine accu- and to document the usefulness of this new method forrately changes in Hct through the skin. The sensor must diagnosis of stenosis, thrombosis, and failure of the vas-be placed directly over the vascular access site in the cular access during routine hemodialysis are warranted.specified orientation to determine relative changes inHct accurately. Additional variability caused by sensor ACKNOWLEDGMENTSplacement does not appear to be significant, however.

Portions of these data were published in abstract form (abstract;The reproducibility of the TQa method in our second Steuer et al, J Am Soc Nephrol 11:300A, 2000) and were presented

at the American Society of Nephrology Annual Meeting, Toronto,study suggests that small variations in sensor placementOntario, Canada, October 12–16, 2000.do not significantly influence the measured vascular ac-

Disclaimer: R.R. Steuer, D.R. Miller, S. Zhang, and D.A. Bell arecess flow rate. An additional concern is whether varia- employees and shareholders, and J.K. Leypoldt is a consultant of In-

Line Diagnostics Corporation.tions in accuracy of the TQa method occur with accessesthat are not superficial or whether the access diameter

Reprint requests to David A. Bell, Ph.D., In-Line Diagnostics Corpo-is very large; however, the spacing of the sensor elements ration, 695 North 900 West, Kaysville, Utah 84037, USA.was designed to minimize difficulties associated with very E-mail: dbell@crit-line.com

large accesses or with deep accesses such as those foundin the upper arm or thigh (abstract; Steuer et al, J Am

APPENDIX 1Soc Nephrol 11:198A, 2000). Less accurate results wouldIn biological tissues, where there is simultaneous absorption andalso be obtained if the sensor did not accurately detect

scattering of light, the intensity of light detected at a photodetectorchanges in Hct due to significant variation in skin pig-(i) is related to the light emitted (i0) by a complex function of the

mentation. It should be noted that the TQa sensor has optical properties of the tissue [32]. We assume that this relationshipcan be expressed over small changes in Hct by the following equationbeen specifically designed to account for the individual[29, 33]:absorption and scattering properties of patient tissues

(discussed previously in this article), and the normalized i � i0 · � · exp(�� · d) (Eq. A1.1)

Steuer et al: Transcutaneous determination of access flow290

where � and d denote the bulk attenuation coefficient and the distance 2% in vascular access blood flow rate when calculated using Equation1 of the main text.between the light source and detector, respectively. For an optical

sensor placed on the skin, the bulk attenuation coefficient is a complexfunction of the attenuation and scattering coefficients of the various REFERENCESlayers of tissue (epidermis, dermis, and subcutaneous tissue) [28, 34].For systems in which light-scattering dominates light absorption within 1. Schwab S, Besarab A, Beathard G, et al: NKF-DOQI clinicalthe tissue, the bulk attenuation coefficient can be approximated by practice guidelines for vascular access. Am J Kidney Dis 30(Supplthe following equation (Steuer et al, unpublished observations): 3):S150–S189, 1997

2. Schwab SJ, Raymond JR, Saeed M, et al: Prevention of hemodialy-� � ( · H � �2

0)1/2 (Eq. A1.2)sis fistula thrombosis: Early detection of venous stenosis. KidneyInt 36:707–711, 1989where and �0 denote a proportionality constant and the time-indepen-

3. Besarab A, Sullivan KL, Ross RP, Moritz MJ: Utility of intra-dent background attenuation coefficient, respectively.access pressure monitoring in detecting and correcting venous out-Differentiating Equation A.1.1 with respect to time and normalizinglet stenosis prior to thrombosis. Kidney Int 47:1364–1373, 1995by the intensity of detected light yields the time-dependent change in

4. Blankestijn PJ, Smits JHM: How to identify the haemodialysislight detected by the photodetector as:access at risk of thrombosis? Are flow measurements the answer?Nephrol Dial Transplant 14:1068–1071, 19991

ididt

� �1��d �

1���2�

dHdt

(Eq. A1.3) 5. Paulson WD, Ram SJ, Birk CG, Work J: Does blood flow accu-rately predict thrombosis or failure of hemodialysis synthetic

Dividing both sides of Equation A.1.3 by (�2 � �02) � H (Eq. grafts? A meta-analysis. Am J Kidney Dis 34:478–485, 1999

1.2) provides an expression for (1/H)(dH/dt) and eliminates the need 6. Paulson WD, Ram SJ, Birk CG, et al: Accuracy of decrease infor determining the factor : blood flow in predicting hemodialysis graft thrombosis. Am J Kid-

ney Dis 35:1089–1095, 20007. Strauch BS, O’Connell RS, Geoly KL, et al: Forecasting throm-� 1

�2 � �20�1i

didt

� �1

2��d �1��� 1

H�dHdt

(Eq. A1.4)bosis of vascular access with Doppler color flow imaging. Am JKidney Dis 19:554–557, 1992

Experimental determination of both the intensity of detected light 8. Lindsay RM, Blake PG, Malek P, et al: Hemodialysis accessand its time derivative permits the evaluation of the following function blood flow rates can be measured by a differential conductivitydefined as F(i,di/dt): technique and are predictive of access clotting. Am J Kidney Dis

30:475–482, 1997F �i, di

dt� �1i

didt

��

(d � 1/�)(�2 � �20)

(Eq. A1.5) 9. May RE, Himmelfarb J, Yenicesu M, et al: Predictive measuresof vascular access thrombosis: A prospective study. Kidney Int52:1656–1662, 1997This function is dependent only on the fractional change in Hct

10. Bosman PJ, Boereboom FTJ, Eikelboom BC, et al: Graft flowand can be used to determine the vascular access flow rate by substitu-as a predictor of thrombosis in hemodialysis grafts. Kidney Inttion into Equation 1 of the main text.54:1726–1730, 1998

11. Bay BH, Henry MI, Lazarus JM, et al: Predicting hemodialysisaccess failure with color flow Doppler ultrasound. Am J Nephrol

APPENDIX 2 18:296–304, 199812. Miranda CL, Sands JJ: Flow volumes as a predictor of hemodialy-

Derivation of an equation to calculate the vascular access flow rate sis access failure. J Vasc Technol 22:73–76, 1998when using the bolus injection, indicator dilution approach is complex. 13. Wang E, Schneditz D, Nepomuceno C, et al: Predictive valuePerl has shown, however, that the constant infusion and bolus injection of access blood flow in detecting access thrombosis. ASAIO Jindicator dilution approaches yield identical results [35]; therefore, 44:M555–M558, 1998we derive below the governing equation from steady-state constant 14. Neyra NR, Ikizler TA, May RE, et al: Change in access bloodinfusion principles [30]. Consider the dialysis circuit in Figure 2, where flow over time predicts vascular access thrombosis. Kidney Inta steady infusion of saline solution occurs in the dialysis venous blood 54:1714–1719, 1998line (ultrafiltration at the dialyzer is neglected). We further assume 15. Sands J: The role of color-flow Doppler ultrasound in the manage-that the outflow resistance at the venous side of the vascular access is ment of hemodialysis accesses. ASAIO J 44:41–43, 1998large; therefore, the injected saline will slow the flow in between the 16. Winkler A, Wuj A, Case T, Ricci M: An experimental study ofarterial and venous needles. Red blood cell balance where the dialysis the accuracy of flow measurements using commercial ultrasoundvenous blood flow enters the access requires: systems. J Vasc Technol 19:175–180, 1995

17. Kult VJ, Scheitza E, Grosswendt J, Klutsch K: Das reale shunt-Ha(Qa � Qb � Qi) � HaQb � Ho(Qa) (Eq. A2.1) volumen subkutaner arteriovenoser fisteln bei chronisch hamodia-lysierten patienten. Z Kardiol 62:158–164, 1973Solving for Qa yields:

18. Gottlieb S, Garcia E, Cold SB, Vanderwerf BA: RadiotracerQa � Qi/�H/Ha (Eq. A2.2) method for nonsurgical measurement of blood flow in bovine graft

arteriovenous fistulas. Proc Dial Transplant Forum 6:107–108, 1976where �H denotes Ha � Ho. This equation describes the relationship 19. Kaye M, Lamaitre P, O’Regan S: A new technique for measuringbetween the vascular access flow rate and relative changes in Hct at blood flow in polytetrafluorethylene grafts for hemodialysis. Clinthe sensor during a constant infusion of normal saline in the venous Nephrol 8:533–534, 1977dialysis blood line. (If ultrafiltration at the dialyzer occurs at a rate of 20. O’Regan S, Lemaitre P, Kaye M: Hemodynamic studies in patientsQf, then the numerator in this equation becomes Qi � Qf.) Noting that with expanded polytetrafluoroethylene (PTFE) forearm grafts.Qi is equivalent to the volume of saline injected in a specified time Clin Nephrol 10:96–100, 1978interval, Equation 2A reduces to Equation 1 in the Methods section 21. Krivitski NM: Theory and validation of access flow measurementduring the bolus injection, indicator dilution approach [30, 35]. by dilution technique during hemodialysis. Kidney Int 48:244–250,

It should be noted that the previously mentioned equations do not 1995apply if a significant stenosis exists between the dialysis needles such 22. Krivitski NM: Novel method to measure access flow during hemo-that the outflow resistance is less than the flow resistance upstream. dialysis by ultrasound velocity dilution technique. ASAIO JIn this case, the injected saline will increase the flow on the venous 41:M741–M745, 1995side of the access, thereby increasing the vascular access flow rate 23. Depner TA, Krivitski NM: Clinical measurement of blood flowunder the sensor. Nevertheless, this condition does not cause substan- in hemodialysis access fistulae and grafts by ultrasound dilution.

ASAIO J 41:M745–M749, 1995tial changes to the analysis and is expected to produce errors less than

Steuer et al: Transcutaneous determination of access flow 291

24. Schneditz D, Fan Z, Kaufman A, Levin NW: Measurement of 30. Lassen NA, Henriksen O, Sejrsen P: Indicator methods for mea-surement of organ and tissue blood flow, in Handbook of Physiol-access flow during hemodialysis using the constant infusion ap-ogy (section 2): The Cardiovascular System (vol III), edited byproach. ASAIO J 44:74–81, 1998Shepherd JT, Abboud FM, Bethesda, American Physiological So-25. Yarar D, Cheung AK, Sakiewicz P, et al: Ultrafiltration methodciety, 1983, pp 21–63for measuring vascular access flow rates during hemodialysis. Kid-

31. Bland JM, Altman DG: Statistical methods for assessing agree-ney Int 56:1129–1135, 1999ment between two methods of clinical measurement. Lancet 1:307–26. Gotch FA, Buyaki R, Panlilio F, Folden T: Measurement of310, 1986blood access flow rate during hemodialysis from conductivity dialy-

32. Cheong W-F, Prahl SA, Welch AJ: A review of the opticalsance. ASAIO J 45:139–146, 1999properties of biological tissues. IEEE J Quan Elect 26:2166–2185,27. Mercadal L, Hamani A, Bene B, Petitclerc T: Determination1990of access blood flow from ionic dialysance: Theory and validation. 33. Cui W, Ostrander LE: The relationship of surface reflectance

Kidney Int 56:1560–1565, 1999 measurements to optical properties of layered biological media.28. Steuer RR, Bell DA, Barrett LL: Optical measurement of hema- IEEE Trans Biomed Eng 39:194–201, 1992

tocrit and other biological constituents in renal therapy. Adv Ren 34. Schmitt JM, Zhou GX, Walker EC, Wall RT: Multilayer modelReplace Ther 6:217–224, 1999 of photon diffusion in skin. J Opt Soc Am [A] 7:2141–2153, 1990

29. Schmitt JM: Simple photon diffusion analysis of the effects of 35. Perl W: Stimulus-response method for flows and volumes inmultiple scattering on pulse oximetry. IEEE Trans Biomed Eng slightly perturbed constant parameter systems. Bull Math Biophys

33:225–233, 197138:1194–1203, 1991