WO2006007840A1

WO2006007840A1 - Method to improve the precision of measured results from a urine bladder monitor

Info

Publication number: WO2006007840A1
Application number: PCT/DK2005/000471
Authority: WO
Inventors: Niels Kristian Kristiansen
Original assignee: Urodan Aps
Priority date: 2004-07-19
Filing date: 2005-07-06
Publication date: 2006-01-26

Abstract

In a method for improving the measured results from an urine bladder monitor, in the sense that errors due to noise in the electronics in the urine bladder monitor, a model of the urine measuring process is created. This model has as input impulses representing a mean flow that at random moments is changed due to the physical parameters, said input is fed to two integrators after which noise from the electronics are added. The resulting output represents a model of the bladder volume, that is corrupted by measurement noise. By using this model it is possible to implement a Kalman Filter that is used for real time measurements.

Description

Method to improve the precision of measured results from a urine bladder monitor.

This invention relates to a method to improve the precision of measured results from a urine bladder monitor.

WO 02/094089 A1 discloses a method and an apparatus for recording the bladder volume in humans or animals.

This method and apparatus are based on an analysis from two or more ultrasounds transducers of the phased array type.

The ultrasound transducers are arranged in a portable fixture, which is attached to a human being or an animal being measured.

The portable fixture is further equipped with a calculation unit, that could be a laptop for a wireless system, that on basis of signals from the ultrasound transducers continuously in intervals from 0,25 - 15 minutes or longer calculates the volume of the bladder.

The precision of the results coming from the calculation system has shown a mean absolute error about 4,8%.

The error originates from the apparatus itself, such as noise coming from side lobes in the ultrasound system, thermal noise from the electronics, pure electronic noise from the electronics calculating the results and quantization noise from the analog to digital converters.

It is therefore an object of the invention to improve the precision of the results derived from the present urine bladder monitor or similar apparatuses.

The object of the invention is achieved by a method of the type defined in the introductory part of claim 1 , which is characterized in comprising the following steps: - creating a model of the bladder measuring process, said model includes the following parameters and calculation units:

- a) feeding to a first integrator a signal w_k consisting of a series of impulses comprising one impulse for the bladder mean flow and a plurality of impulses representing random physical events said events are derived from independent driving functions, such as temperature, activity fluid intake etc.

- b) feeding to a second integrator, the output from the first integrator a signal fk comprising a mean flow from the kidneys to the bladder that at random moments is changed as a consequence of physiological parameters in a random way:

- c) said output Xi,_k from the second integrator represents a model the bladder volume that is corrupted by measurement noise Vk resulting in a signal ZR.

In this way it is possible to implement a filter that is used for real measurements in which it is possible to track and compensate noise errors coming from measurements errors.

By using this method the precision of the results derived from the urine bladder monitor, in the sense that mean absolutely error in the measured results are improved, since the measurements errors are incorporated in the calculations.

A filter that is especially suitable for implementing the method, is a filter as defined in claim 2, i. e. a Kalman Filter.

As stated in claim 3, the errors from the measuring system are assumed white and generated from several independent sources, such as thermal noise from the electronics in the measuring system.

Finally an expedient embodiment of the method is, as stated in claim 4, that in case of micturition during the measuring process the Kalman filter is reset, and the filtering process is restarted.

The invention will now be explained more fully with reference to the drawing, in which:

fig. 1 shows a block diagram for a model circuit according to the invention,

fig. 2 shows a signal at the output from a first integrator on fig. 1 ,

fig. 3 shows a signal at the output from a second integrator on fig. 1 ,

fig. 4 shows the measured results from tree patients before and after being filtered with a Kalman filter,

fig. 5 shows the same as fig. 4 but for another tree patients, whereas

fig. 6 shows how to deal wit the measurements in case of a micturition during the measuring process.

On fig. 1 , 1 designates an integrator that at its input is supplied with a signal W_k consisting of impulses representing a mean flow that is mixed with some physiological parameters occurring in a random way. These random parameters occur from a patient's temperature, physical activity, etc. The output from the integrator 1 gives a signal f_k representing a modeled mean flow that at random moments is changed in a random way from the kidneys to the bladder at time k said is shown on fig 2 where the maen flow is denoted 4 whereas the random changes in flow are denoted 5. The signal fjs fed to another integrator 2.

The output from the integrator 2 is denoted X₁^ representing the volume in the bladdet at time k.

The signal Xi,_k is shown on fig. 3 and denoted 7.

To the output from integrator 2 an error signal denoted VK, is added to Xi,_k in a summing unit 3. The output from the summing unit 3 is denoted Zk that represents a model of the bladder volume measured measured by the bladder volume monitor or a similar apparatus.

This signal represents a urine bladder volume vs. time from a patient including physiological parameters that originates from a patients

^•temperature, physical activity, noise errors from the electronics involved in the apparatus used for measuring the bladder volume etc. The Kalman filter 4 shapes the signal 7 on fig. 3 in such a way that the mean absolute error in the measured values due to errors in the measurements are reduced, cf. also later the more theoretical discussions later.

Fig. 4 and 5 shows measured urine bladder volume from 6 patients. For each patient a white and a black symbol represent a measured value before (the black) and after (the white) the Kalman Filter.

On fig.4, the signal 9 is divided in black symbols 10 and white symbols 9.

It is clear that the signal 9 represented by the white symbols as more smooth than the signal represented by the black symbols 10. From the signal 11 on fig. 1 it is clear the even when the results from measuring process incorporates big fluctuations, then the Kalman filter is able to smooth the signal.

On fig. 6 it is shown that if a patient during a measuring process micturate, then the measuring process will be restarted. In the following, a more theoretical approach to the invention will be explained.

This involves a Kalman filter procedure for tracking urinary bladder filling from intermittent bladder volume measurements made by an ultrasonic bladder volume monitor. The implemented Kalman filter was based on a double integrator as a model for the bladder filling process between micturitions and included a procedure to reset the filter in the event of a micturition. The performance of the Kalman filter was . evaluated experimentally using an ultrasonic bladder volume monitor on seven male urologic patients. During cystometry, saline was infused into the patient's bladder with a constant rate of 30ml/min until it was full while the volume of the bladder was recorded every 30s by the bladder volume monitor. The evaluation showed that the filter significantly improved the precision of the measured volumes in terms of mean absolute error by 4.2 ml (95% Cl: 0.7- 7.7 ml) (p=0.025) without affecting the system accuracy, i.e. slope (p=0.92) and intercept (p=0.32). Finally, the micturition reset procedure was verified using simulated data.

Intermittent or near-continuous monitoring of urine bladder volume over extended periods of time may be valuable in management and diagnostics of various urologic disorders such as nocturnal enuresis and neurological diseases. Furthermore, urinary bladder volume monitoring may be of value in the study of urine production regulation and basic mechanisms of both urologic and non-urologic disorders as well as during validation of new pharmaceuticals, e.g. with regard to diuretic or anti-diuretic properties or side effects.

A test in a previously designed and evaluated an ultrasonic bladder volume monitor, cf. also WO 02/094089 A1 , intended for monitoring children with nocturnal enuresis during the night, showed that the syste.m had an adequate precision with a mean absolute error of 4.8%. However, it is an object to enhance this precision to improve the ability of the bladder volume monitor to estimate volume increments, i.e. urine production, with higher accuracy. This will be done by taking into account that a monitor system that intermittently samples bladder volume obtains more information about the bladder that simply the sum of the information from the individual measurements provided that typical bladder filling behavior and measurement errors characteristics are known.

An effective method of tracking the state of a dynamic system in the presence of noise is the Kalman filter. This filter, which is an estimator for the linear-quadratic-Gaussian problem, consists of a collection of mathematical equations that recursively estimates the state of the system such that the mean of the squared error is minimized. The Kalman filter approach is therefore suitable for urinary bladder volume tracking based on intermittent ultrasonic measurements of bladder volume and in the following preliminary experimental results obtained in an urodynamic investigation setting are also present.

Fundamentally, it is assumed that the observed instantaneous bladder volume xi,_k is produced through a linear process. The flow of urine from the kidneys to the bladder (f_k) is modeled as a mean flow that at random moments is changed in a random way. Consequently, the urine flow filling the bladder is modeled using an integrator as shown in figure 1 and described by equation (1). The integrator is driven by a random process W_k described by equation (2). Here, a_n for n≠O is empirically approximated to a truncated gaussian random variable with a zero mean and a variance of σ_a ² (most often σ_a<a₀), as urine production is a function of many independent driving functions, e.g. temperature, activity, and fluid-intake, within certain physiological limits. It seems reasonable to assume that W_k is white such that the autocorrelation function will be: R_w,π= σa²δ_n. In an observation period starting at k=0, W_k is thus a start impulse with the amplitude a₀, equal to the mean flow to the bladder, added to a fragment of a stationary white process representing the random flow variations.

n≠O

Urinary bladder volume xi,k as a function of time k is now found by integrating the flow to the bladder f_k as described in equation (3) assuming that no voiding or leakage from the bladder occurs.

When bladder volume is measured using a bladder volume monitor or other scanning devices, the measurement will be somewhat corrupted by noise. This noise is generated by several independent sources inherent to the measurement system such as errors in the ultrasound system due to side lopes, thermal noise from the electronics, and quantization noise from the analogue-to-digital converter. The sum of the measurements errors V_k is assumed to be white and independent on the bladder volume XI ,R. This assumption is based on an analysis of the total system and verified through empirical observations. The complete model of the observed system is depicted in figure 1. It is noted that the model is equivalent to that for which the Kalman filter was developed. A Kalman filter operates by minimizing the mean of the squared error: E[(x_{l k} -x_u)²] where x_{I k}is an estimate of X₁ ,_k determined from the observation of Z_k. The Kalman filter has been chosen for this application because it is relatively easy to implement, execute, and control with regard a degree of filtering.

The state of the bladder system at time k is described as shown in equation (4); where XR = [xi,k X2,k]^τ, Xi,k is the volume of the bladder at time k, and x₂,ι_< is the volume at time k-1. Furthermore, W_k is the driving process noise at time k. The coefficient matrix A along with matrix B, which relate.s the noise input to the system state, can be deduced from figure 1 and described as shown in equation (5).

X₄ = A -X₄^B - W₄ (4)

A = (5)

Equation (6) describes the measurement procedure, where Z_k is the volume measurement at time k; H = [1 0] relates the state vector to the measurement, and V_k is the measurement noise, which is assumed to be gaussian with zero mean and a variance of R.

Z₄ = H - X, + v_k (6)

The process noise variance σ_a ² also denoted Q was estimated to be «1. However, the exact value must be determined through further investigation. Furthermore, through analysis of measurements performed on bladders with known volumes, the measurement noise variance, R, was estimated to be approx. 10.

The discrete Kalman filter is implemented using two sets of equations; (1 ) the time update equations and (2) the measurement update equations. The time update equations (7) and (8), estimate a priori system state and error covariance one time step ahead, i.e. from k-1 to k. Here, x^~ is the a priori state estimate at time k, x_t_, is the a posteriori state estimate at time k-1, P_λ ^~ is the a priori estimate error covariance at time step k, and P^₁ is the a posteriori estimate error covariance at time k-1. The a priori and a posteriori error covariances are defined as P^ = EIe^ -e[^~)T], where e^ =x_k -x<^~' .

P; = A - P_t_, A^r +B Q B^Γ (8)

The measurement update equations, reproduced as equations (9)-(11), first calculates the Kalman gain, Kk, from the a priori error covariance and the measurement noise variance. This gain is then used to calculate the a posteriori state estimate from the a priori state estimate and the measured volume at time k, Z_k. Finally, the a posteriori error covariance is calculated using the a priori error covariance and the Kalman gain.

K_t = P; -H^r -(H-P- -H^r +R)^~1 (9)

x_k = x_k +K_K - (_k -U-r_k) (10)

P₁ = (I-K, H) P,^" (11)

The Kalman filter equations were implemented in C++ and used in conjunction with our existing PC-based bladder volume monitor signal processing previously described. To optimize bladder volume tracking immediately after micturation, the filter a posteriori state, i.e. x_Uk and χ_{2 k} , was reset to the current measurement, i.e. z_k, if the filter input was lower than 25% of the output, thus indicating that micturation had occurred. The filter was equally reset to zero at negative output values. To 'insure fast initial adaptation, the two first measurements were used as initial values (guesses) for Jc_{1 k} and x_2Λ whereas the third measurement was used as the initial input for the filter.

The Kalman filter was evaluated on bladder volume measurements made in seven male urologic patients during cystometry. The patients had their bladders filled with saline with a constant rate of 30ml/min through a urethral catheter (ch 8) until maximal capacity while the bladder volume monitor measured the bladder volume every 30s. The seven patients presented in this paper were selected from a pool of 11 male patients. Data from four patients were excluded because of measurement problems unrelated to the Kalman filter, e.g. imported air into the bladder or heavy obesity. The filtered and unfiltered bladder volume measurements were analyzed by means of linear regression analysis. The differences in slope, intercept, and mean absolute error (relative to the individual regression line) were analyzed for significance using one sample t-test.

To evaluate the performance of the filter in the event of a micturition, the volumes measured in patient no. 2 were feed through the filter twice without delay and the result visually evaluated.

The results from the experimental verification of the implemented Kalman filter are presented in table I and illustrated in figure 4 and fig. 5, which shows filter input and output for each patient. Linear regression: analysis of the bladder volume signals performed before and after Kalrrian filtering showed no change in slope (p=0.92) or intercept (p=0.32). Precision in terms of mean absolute error relative to the individual regression line was significantly improved by 4.2 ml (95% Cl: 0.7-7.7 ml) (p=0.025). Finally, figure 6 seems to indicate that the filter is properly reset in the event of a micturition.

This shows that a urinary bladder monitor system that periodically measures bladder volume can get a more precision view of bladder filling if typical bladder filling behavior and measurement errors characteristics are known beforehand and taken into account. A Kalman filter was used to track the state of bladder filling in the presence of white measurement noise based on a mathematical model of the bladder filling process. A double integrator was chosen as a suitable model due to its ramp signal impulse response, which mimic the steady filling process usually seen at least between micturitions. The bladder volume is most likely to increase at a steady rate until the bladder is more or less completely emptied. The experimental evaluation showed that the Kalman filter did not affect accuracy since both slopes and intercepts from the linear regression analysis were not significantly changed by the filter. However, precision in terms of mean absolute error was significantly improved for the filtered data compared to the unfiltered data. The improvement in precision was observed for all patients expect patient no. 3. Figure 3 shows that the filter seems to track the bladder volume of patient no. 3 precisely. However a small bend in the curve results in a smaller error for unfiltered data than the filtered data compared to a straight line. During monitoring of patient no. 1 , the monitor was erroneously placed to low such that the symphysis pubis obscured some the field-of-view of the monitor. Consequently, both accuracy and precision have been greatly affected. In this patient, the effect of the Kalman filter is clearly observed; the filter tries to keep the bladder volume filling steady in spite of very noisy measurements. Finally, the evaluation showed that the Kalman filter was properly reset in the event of micturation as shown in figure 6. This part of the evaluation was, however, done using simulated data by feeding the volumes measured in patient no. 2 through the filter twice, thus simulating that micturition had occurred between two measurements.

A major advantage of using the Kaiman filter for this application instead of another digital method, e.g. a FIR filter or an NR filter, is the absence of group delay. A bladder volume monitor must often operate in real time, e.g. when using the monitor as an alarm to signal that an enuretic event is imminent or that a catheterization should be performed to avoid bladder distension. Normal operation of the monitor would demand a measuring period in the order of minutes, thus making a delay of only a few samples intolerable. The cost of adding the Kaiman filter to the present PC-based system, e.g. with regard to code size and execution time, is very limited. Furthermore, a bladder volume monitor system warrants an interval between measurements in the order of minutes leaving plenty of time for advanced signal processing methods.

The Kaiman filter presented was evaluated in patients during cystometry with an abnormal bladder filling rate of 30ml/min and not during normal bladder filling, which might limit the applicability of the results. However, the use of cystometry during the evaluation of the bladder volume monitor provides a very practical method of testing the system over a large range of volumes. Nevertheless, additional examination and tuning of the filter should be performed using data from patients during natural bladder filling; preferably during extended periods of time such that the filter performance can be evaluated in the presence of the normal diurnal rhythm of urinary output. However, during this experimental evaluation, we did use a reduced interval between measurements to compensate for the increased bladder filling rate. Furthermore, since only data from male patients was used, future evaluation of the filter should also include females. In patients 2-5 and 7, the slope ranged from 26.9-36.7ml/min. Differences between this slope and the rate of infused volume can be explained by natural urine production along with the fact that the remaining signal processing software has been only roughly calibrated. Therefore, for accurate absolute measurements, the signal processing software should be more precisely calibrated based on data from a large number of subjects. In patient 1 , the slope was abnormally low due to erroneous placement of the apparatus, whereas the slope in patient 6 was high at =49ml/min probably partly due to a high urine production during the examination. However, further investigation into the absolute accuracy of the bladder monitor is needed.

A Kalman filter for bladder volume tracking was successfully implemented based on a double integrator model of the bladder filling process. Experimental evaluation performed in seven male urologic patients during cystometry showed that the filter significantly improved precision of the measured volumes without affecting system accuracy.

Tables

Table I. The slopes and intercepts from the linear regression analysis performed before and after filtering along with mean absolute error relative to the individual regression for each patient.

Before filter After filter Change

Patient 1 : Slope (ml/min) 20.3 20.9 0.6

Intercept (ml) -28.4 -36.7 -8.3

Mean abs. error 21.8 16.2 -5.6

(ml) •

Patient 2: Slope (ml/min) 31.9 31.9 ^! 0.0

Intercept (ml) 54.1 55.4 1.3

Mean abs. error 16.6 15.2 -1.4

(ml)

Patient 3: Slope (ml/min) 27.0 26.9 -0.1 Intercept (ml) 22.7 22.8 0.1

Mean abs. error 11.2 11.6 0.4

(ml)

Patient 4: Slope (ml/min) 27.1 28.8 1.7

Intercept (ml) 4.2 -5.6 -9.8

Mean abs. error 16.3 12.1 -4.2

(ml)

Patient 5: Slope (ml/min) 36.7 35.7 -1.0

Intercept (ml) -18.8 -10.4 8.4

Mean abs. error 30.4 19.6 -10.8

(ml)

Patient 6: Slope (ml/min) 47.0 49.2 2.2

Intercept (ml) -8.8 -25.2 -16.4

Mean abs. error 12.0 10.3 , -1.7

(ml)

Patient 7: Slope (ml/min) 33.0 29.0 -4.0

Intercept (ml) -19.5 -18.7 0.8

Mean abs. error 17.3 11.1 -6.2

(ml)

Claims

1. Method to improve the precision of measured results from a urine bladder monitor characterising in comprising the steps of:

- creating a model of the bladder measuring process, said model includes the following parameters and calculation units:

- a) feeding to a first integrator (1) a signal w_k consisting of a series of impulses comprising one impulse for the bladder mean flow and a plurality of impulses representing random physical events, said events are derived from independent driving functions, such as temperature, activity fluid intake etc.

- b) feeding to a second integrator (2) the output from the first integrator a signal f_k comprising a mean flow from the kidneys to the bladder that at random moments is changed as a consequence of physiological parameters in a random way:

- c) said output xi,k from the second generator represents a model the bladder volume that is corrupted by measurement noise Vk resulting in a signal Z_k.

2. Method according to claim ^ ch a racte ri s i n g^' in that the model according to claim 1 is used to implement a Kalman filter.

3. Method according to claims 1 -2, characterising in that the errors from the measuring system are assumed white and generated from several independent sources, such as thermal noise from the electronics in the measuring system.

4. Method according to claims 2-3, characterising in that in case of micturition, during the measuring process, the Kaiman filter is reset, and the filtering process is restarted.