A novel quantitative method for measuring obstruction in the upper urinary tract: The ‘obstruction coefficient’


Sandor Lovasz md, Department of Urology, Semmelweis University, Ulloi Str. 78/B, 1136 Budapest, Hungary. Email: lovasz.sandor@chello.hu


Objectives:  To define an exact pressure-flow correlation in the upper urinary tract using an improved measurement method, to quantitatively characterize the degree of postrenal obstruction and to find a simple way of calculating it in everyday urological practice.

Methods:  The data of 112 cases were included in the analysis. The dynamic method of a multistep, constant pressure perfusion study was used to precisely measure a wide range of pressure-flow dependences. Values of established parameters measuring the degree of obstruction were compared: the intrapelvic pressure, the ureteral opening pressure and the newly introduced ‘obstruction coefficient’.

Results:  Pressure-flow relations can be best presented by a parabolic curve described by the simple formula Y = AX2 + B. Depending on the degree of obstruction, the shape of this curve can be characterized by a single number, that we defined as the ‘obstruction coefficient’. Computer-based evaluation software for the easy calculation of this coefficient is presented here and freely available on demand. The Whitaker-test, the ureteral opening pressure, and the ‘obstruction coefficient’ showed significant correlation proving that the latter was clinically applicable in measuring the degree of obstruction.

Conclusion:  Calculation of the ‘obstruction coefficient’ enables us to exactly define the degree of upper urinary tract obstruction and to safely monitor for a long period conditions inhibiting ureteric passage.


For a long time, it has been desirable in urology to measure the degree of organic or functional ureteric obstruction determining the emptying of the kidneys. The rate of the obstruction was first concluded from the morphological deformities triggered by obstruction. Selective urography and ultrasound examinations were performed since experts supposed that the rate of the dilatation of the collecting system was proportional to the degree of obstruction.1,2 The overwhelming spread of ultrasonography led to the birth of the method of diuretic ultrasonographic examinations,3 where the rate of pelvic dilatation caused by enhanced diuresis was observed. In addition, an isotope examination of the kidneys, that is, dynamic renography, was complemented by diuretic charge. The method of diuresis renography enabled us to determine obstruction semiquantitatively.4–7 A resistive index helps conclude the rate of obstruction in a non-invasive way either determined by duplex Doppler sonography,8–10 computerized tomography,11 or by magnetic resonance imaging.12 This method could not spread widely, however, due to the sophisticated equipment needed, the great interpersonal differences between examiners, and because the results do not always correlate with clinical figures. Both the normal range of a resistive index and a resistive index ratio, and the reliability of their threshold values as prognosticators of true obstruction in the upper urinary tract (UUT) are still debated.13

Bäcklund et al. were the first, in 1965, to estimate the degree of ureteric obstruction by a perfusion provocation study measuring pressure and ureteric flow in the UUT.14 The method was popularized by Marshall and Whitaker15 in 1975, later known as the Whitaker test (WT). Using a puncturing needle, researchers perfused the collecting system at a 10 mL/min constant flow rate and measured the pressure in it. They concluded the obstruction rate from the elevation of intrapelvic pressure (IPP) during external filling. Moreover, in cases of moderate or increased incomplete occlusion, the filling rate at 10 mL/min would lead to unlimited IPP elevation with dangerously high over-pressures causing calyco-tubular reflux with consequent iatrogenic pyelonephritis. In these situations, the degree of obstruction cannot be measured due to continuously increasing IPP. Therefore, the WT could not disseminate due to the complicated and expensive equipment, to the invasiveness of the method, and the possibility of severe intrapelvic over-pressures.

In order to fill in the gaps of the WT, independently and almost at the same time Vela-Navarrete and Ripley published a method of pressure-flow studies using constant filling pressure.16,17 The flow triggered by a constant filling pressure was measured, and they found that this was proportional to the degree of ureteric obstruction. This method of pressure-flow measurement has become known as the Vela-Navarrete test (NT).18 The NT is a more exact method, where no overpressure can occur and it is able to provide reliable, evaluable results even in cases of severe obstruction.

Constant pressure perfusion applied during pressure-flow studies was demonstrated to provide increased sensitivity and better discrimination between normal and partially obstructed systems relative to constant flow pressure measurements.19,20

Pressure-flow studies performed at different filling rates may detect outflow obstruction in a more reliable way.19,20 Many authors have found and suggested a linear correlation in pressure-flow dependence.16,19,21,22

Wåhlin et al.19 suggested defining mean ureteric resistance where measurements were performed at three different filling pressures and resistance defined as pressure divided by obtained flow. This already refers to a non-linear correlation.

Another parameter was found to quantify postrenal obstruction, the ureteral opening pressure (UOP)23 defining it as the IPP at which the contrast agent is first seen beyond the suspected site of obstruction at antegrade pyelography. UOP and WT proved to show a good correlation.

We have set the following main goals for this study:

  • 1To work out the best method of pressure-flow studies to gain precise, evaluable data of pressure-flow dependence in a wide range, up to 20 mL/min;
  • 2To identify the shape of pressure-flow dependence by a possibly simple mathematical formula and to find a generally useable quantification method of the degree of obstruction;
  • 3To develop freely available evaluation software that may aid spreading pressure-flow studies in UUT;
  • 4To compare the three different methods for quantifying postrenal obstruction: WT, the UOP, and our suggested new parameter, the obstruction coefficient (OC).


All of our urodynamic measurements were performed using a variant of the model Ellipse equipped with additional pressure and drop sensors and an evaluation-software for urodynamic measurements in the UUT developed in cooperation with Andromeda Ltd. Germany. It allowed us to perform both constant flow pressure studies (Whitaker principle) and constant pressure perfusion studies (Vela-Navarrete principle).

Existing single-lumen nephrostomy catheters were used for pressure-flow studies. We integrated real time resistance compensation into the software of Ellipse.24 There was therefore no need to insert two separate needles or catheters, nor a double-lumen urodynamic catheter. In order to treat the insufficiency of WT and NT mentioned earlier, we worked out a multistep, dynamic method of urodynamic study of the UUT, which lets us record a wide range of the pressure-flow curve more precisely.

Pressure-flow studies were performed by constant pressure perfusion based on Vela-Navarrete's principle (Fig. 1), by gradually raising filling pressures, immediately after the emptying of the bladder by the patient.

Figure 1.

Sketch diagram of constant pressure perfusion measurements by adjustable filling pressure, the Vela-Navarrete principle.

Flow rate was measured by a drop sensor and pressure was measured outside the body, at the pelvic level. At each filling pressure, mean values of the filling flow rate and calculated IPP between two markers were calculated when a steady state had been reached (no more subsequent change in flow and IPP).

Basal IPP (pressure measurable at the empty pelvis) was used as reference pressure therefore no urethral catheterization was needed.

To achieve a measurable external filling flow, the filling pressure must exceed the spontaneous intrapelvic pressure (SIPP), the IPP measured at spontaneous diuresis as internal flow. The first filling pressure was set on SIPP plus 5cmH2O and we elevated the hydrostatic filling pressure (the height of the infusion bottle) by 5cmH2O at each subsequent step. The upper limit of filling pressure was set to basal IPP plus 30cmH2O because higher pressures could have caused pain to the patients or even calico-tubular reflux increasing the risk of iatrogenic infections. At each filling pressure, when a steady state was reached (no further change in pressure or in IPP), mean filling flow-rate and calculated IPP were registered and all steps were digitally saved on a PC running AUDACT software v.6.05 (Fig. 2).

Figure 2.

Multistep, constant pressure perfusion study; flow curve based on drops; measured pressure, resistance and calculated real intrapelvic pressure (IPP) from up to down respectively .

Based on mean flow rates and corresponding calculated mean IPP, the pressure-flow curve was calculated with the aid of our newly developed PC software.

From the acquired pressure-flow curve, we calculated the IPP value at a 10 mL/min filling rate (virtual WT). The correlation between the calculated values of UOP, virtual WT, and the coefficient characterizing the shape of the curve, thus the rate of obstruction, was then statistically analyzed.

One hundred and twelve patients with signs of postrenal obstruction were included in the urodynamic studies of the upper urinary tract (UDUUT), performed using constant pressure perfusion filling in a multistep manner. Measurements were performed in patients with free outflow or clinically incomplete obstruction. This was defined as dilation of the collecting system seen on ultrasound or X-ray and a SIPP lower than 30cmH2O over basal pressure, and/or if the contrast agent flowed down into the bladder at antegrade pyelography performed by a controlled filling pressure less than 30cmH2O over basal pressure. Demography data of the 112 patients were: 46 female and 42 male patients; in 8 female and in 16 male patients data of repeated tests were also taken into account as tests were performed after a longer period, in a different clinical situation. The mean age was 53 years (19–76). All patients were previously deviated by a percutaneous nephrostomy catheter 2–32 days before time of measurement.

Indication of nephrostomy placement for temporary urine deviation is listed (Table 1).

Table 1.  Indication of nephrostomy placement in patients of urodynamic studies of the upper urinary tract (UDUUT)
No. patientsIndication of percutaneous nephrostomy placement
23Percutaneous stone removal
16Ureterorenoscopic stone disintegration
16ESWL of large ureteric stone
13Stricture of p-u junction
12Pelvic dilation of unknown origin
11Incomplete ureteric compression caused by metastasis of malignant tumors of pelvic organs
10Ureteric obstruction caused by bladder tumor
9Worsening of function of dilated transplanted kidneys due to ureteral kinking or stone, or stenosis of uretero-ureteral anasthomosis
2Anasthomosis-stenosis of uretero-sigmoideostomy

All urodynamic studies performed in the last 3 years was based on the permission of the Regional and Institutional Committee of Science and Research Ethics of the Semmelweis University of Budapest, Hungary (TUKEB 72/2004). Patients declared their agreement by signing the Patients' Information sheet (informed consent).


Both filling flow curves and pressure curves may show great variations in time. These regular waves are due to rhythmic pelvic contractions or can be signs of ureteric peristalsis. These quick and great changes in measured values practically hinder the visual estimation of mean values. To solve this problem and to make the calculation of mean values exact, we integrated a software solution into our program, which automatically calculates mean values of flow and pressure between two adjustable markers (Fig. 3).

Figure 3.

Digitally registered flow curve of diuresis; drops, flow curve (Qfill) and measured pressure (Pmeas); in central window: volume (Vinf), mean flow (Qave) and mean measured pressure (Pmeasave; due to ‘suction’ it is negative) of urine produced between two markers (US [urodynamic evaluation starts], UE [urodynamic evaluation ends]).

Due to the method of using a single lumen catheter and an external pressure sensor, the resistance of tubing and catheter between the pressure sensor and the renal pelvis must be subtracted from measured pressure values to calculate real IPP, as described by Ripley and Somerville.16 True IPP can be calculated according to the following correlation: IPPtrue = Pmeasured − Presistance.

As the resistance is flow dependent, manual calculation of real IPP could just be performed afterwards and would take much time and energy. Therefore, we integrated a compensation of resistance on the basis of actual flowrate into the software of our Ellipse variant so that we could display and document the flow curve (Qfill), the measured pressure (Pmeas), the calculated actual resistance (Presist) and the calculated actual IPP simultaneously, in real time (Fig. 4).24

Figure 4.

Real time resistance compensation by integrated Ellipse software. If external filling is stopped, calculated intrapelvic pressure (IPP) equals the externally measured pressure.

Although the pressure-flow correlation seems to be close to linear especially if measured in a narrow range of flow, a regression analysis of the data of 112 multistep pressure-flow studies showed that the quadratic term is highly significant (P < 0.05). The adjusted R2 values are 0.715 for the linear and 0.889 for the quadratic model. The second one is clearly superior. Therefore, the appropriate, exact description of pressure-flow correlation needs a quadratic model so that it can be well described using the simple formula Y = AX2 + B in a wide flow range (Fig. 5).

Figure 5.

Parabolic curve characterizing pressure-flow dependence during pressure flow studies of the upper urinary tract (UUT).

A is the coefficient determining the shape of the curve, and is in accordance with the level of obstruction, therefore we call it the obstruction coefficient. B stands for UOP, which we define as the minimal IPP at which ureteric flow is just starting. Its value also depends on obstruction (Fig. 6).

Figure 6.

Shapes of different pressure flow curves corresponding to different values of obstruction coefficient (OC; A) and different levels of ureteral opening pressure (UOP) in accordance with rates of obstruction.

We developed easy to use, PC-based evaluation software that calculates the parabolic curve of pressure-flow relation immediately. After the data has been filled in, this program displays a parabolic curve graphically and calculates the OC (A) and UOP (B) numerically. Due to the variance of data, the curve may not pass through all points directly; however, it closely approximates them through the method of least squares. It displays measured points, the best fitting parabolic curve, the mean value of their difference as an average error, pointing out the maximal error (Fig. 7). Moreover, the software is also capable of recording all measured data, calculated pressure-flow curve, OC, and UOP for future evaluation.

Figure 7.

Freely available, PC based evaluation program for easy calculation of the obstruction coefficient (OC). Average error is calculated and data showing greatest deviation is automatically marked.

We compared OC values of 112 multistep, constant pressure perfusion studies with their IPP values corresponding to 10 mL/min flow values of the pressure-flow curve (virtual WT) and the IPP values at zero flow (UOP) (Table 2).

Table 2.  Correlation analysis of the †obstruction coefficient (OC), ‡the virtual Whitaker test (WT) and the §ureteral opening pressure (UOP).
Correlations (OC_WT_UOP)
Marked correlations are significant at P < 05000 n = 112 (casewise deletion of missing data)

Correlation analysis of these data proved that correlation between any two variables is significant, it is weak between OC and UOP and it is as close between OC and WT as it is between UOP and WT. This can be well demonstrated in a 3D scatterplot of variables (Fig. 8).

Figure 8.

3D scatterplot of the correlation of variables during pressure-flow studies of upper urinary tract (UUT).

This way we could indirectly prove the clinical applicability of OC as a quantitative measure.


All measurements were carried out through nephrostomy catheters being already inserted. In order to use existing nephrostomy catheters for pressure-flow studies, we need to perform a resistance calibration of the tubing and catheter saved into the BIOS of the urodynamic equipment. The solution of automatic, real-time resistance compensation allowed us to reduce the invasiveness of urodynamic studies of the UUT and to widen the indication of these examinations.24 This method also permitted us to collect a sufficient database for statistical analysis and to prove parabolic pressure-flow dependence.

In order to avoid the confusing influence of intravesical pressure on IPP, all measurements were performed immediately after spontaneous emptying of the bladder. Low intravesical pressures observed at low filling volumes (under 100 mL) had no influence on pressure relations of the UUT when vesicoureteral reflux could be ruled out.

We performed pressure-flow studies in accordance with the concept of a constant pressure perfusion study (Vela-Navarrete principle), because constant flow pressure study (WT) cannot provide an acceptable result in cases of expressed obstruction. This is because the un-physiologically fast filling rate may hamper us from reaching a steady state in IPP and ureteric flow during perfusion. IPP is continuously increasing in these cases; therefore, the examination must be stopped. This fact cripples the applicability of WT.

The pressure-flow curve based on changes of IPP and ureteric flows during dynamic (multistep) pressure-flow studies is independent from the reference pressure therefore one of the advantages of this method is that there is no need to determine the reference pressure at all.

The many data we obtain with multistep studies also reduce uncertainty caused by natural measurement failures. This way we can define pressure-flow curves much more exactly which presents another advantage of this method.

The presentation of the parabolic curve and the calculation of the OC requires a mathematical analysis (especially considering that measured values are not always exact due to errors of measurement), therefore this complicated and time-consuming calculation cannot be established in everyday clinical praxis and it would be an obstacle to the spreading of the method for a quantitative determination of obstruction. In order to overcome these difficulties, we introduced a PC-based evaluation program.

The calculated OC, the clinical picture and the antegrade pyelo-ureterographic X-ray records showed good correlation. Based on these comparisons we have concluded that under the value of 0.03 free ureteric passage may be supposed, with neither clinical nor X-ray reference to obstruction, while the obstruction is moderate up to a value of 0.08, and it is significant above it.

In order to get calculations as exact as possible, we have to find out the real flow rate inside the ureter, as diuresis of the examined kidney adds to the external perfusion rate as intrinsic filling. Therefore we always try to keep diuresis as low as possible, as spontaneous diuresis <1 mL/min has just negligible effect on the results of measurement. If observed diuresis of the kidney is higher than 2 mL/min, then its exact mean value should be calculated using the mean value calculation as already described (Fig. 4) and should be added to external filling rates.

Reaching higher flow rates during perfusion, ureteric peristalsis hampers ureteric flow more and more, and flow resistance increases. To maintain higher flow rates, ureteric peristalsis increases bolus volumes, which will once confluence at a certain flow rate; consequently, the ureter becomes a continuous pipe while flow resistance suddenly, dramatically decreases and further pressure elevation brakes.8,25 Therefore, the evaluation software can only be used within a certain range of ureteric flow, according to our experience, up to a 20 mL/min flow rate. A sudden decrease of pressure at a high flowrate proves this situation and this pressure value should not be considered during calculation.

High levels of IPP during the measurement may also induce other forms of measurement bias, such as hysteresis and/or leakage.19 Therefore, the upper limit of flow was drawn at 20 mL/min in our studies and the pressure limit, at 30cmH2O over basal IPP.

During all of the measurements we calculated the OC, the UOP, and the virtual WT values. This latter may need some explanation. As we did not use constant flow pressure studies for our measurements due to their above-mentioned disadvantages, we could not get true WT values. However, as we were able to gain very exact pressure-flow curves during our measurements, IPP values corresponding to the 10 mL/min filling flow rate could be defined. We call this level of IPP virtual WT (Fig. 9).

Figure 9.

Explanation of the obstruction coefficient (OC), the virtual Whitaker test (WT) and ureteral opening pressure (UOP) compared in the study.

In 36/112 (29.5%) cases WT was not evaluable, as a steady, measurable pressure state could not be reached due to continuously growing IPP. Wåhlin reported an even higher proportion of 39/46 (85%). Patients' selection may have accounted for such a huge difference, as we were performing our studies just before the planned removal of nephrostomy catheters and most of them were not obstructed any more, whereas all of Wåhlin's patients had hydronephrotic kidneys due to postrenal obstruction.

An exact, quantitative determination of postrenal obstruction offers even more benefits compared to the use of relative categories of obstruction (mild, medium, expressed, etc.), since it enables us to recognize and document any changes in the processes influencing ureteric flow. It is capable to quantify any ureteric obstruction caused by scarification or external compression of malignant tumors and to measure the effectiveness of therapy. Repeated examinations in supine and standing positions can prove the effect body position has upon ureteric obstruction in cases of ptotic and transplanted kidneys.

UDUUT are appropriate examinations precisely determining the degree of postrenal obstruction. By using our newly developed multistep method of urodynamic examinations of the UUT, we can measure a wide range of pressure-flow dependence under changing flow rates and changing pressures. We have proved parabolic correlation described by the formula Y = AX2 + B in a flow range of up to 20 mL/min. We introduced the OC characterizing the degree of obstruction quantitatively, by a single number. This enables us to monitor obstructing processes over a longer period objectively.

We present new, PC-based software for the simple calculation of the obstruction coefficient. The software is freely available on demand. We do hope that with the help of our method and software we can provide a more precise measuring method which might help detect the degree of obstruction in a more exact way, to the benefit of our patients.


Our thanks are due to Michael Gondy-Jensen, Andromeda Ltd. for incorporating compensation routine into the BIOS of the urodynamic equipment Ellipse and to Professor Sandor Kemeny for statistical analysis of our data.