Computer Programs in Biomedicine 5 (1975) 5-10 © North-HoUand Publishing Company

STATISTICAL ANALYSIS AND GRAPHICAL REPRESENTATION OF THE TEMPORAL AND DISTRIBUTIVE PROPERTIES OF URODYNAMIC DATA Mark SILVERT and Christos CONSTANTINOU Division o f Urology, Stanford University Medical School, Stanford, California 94305, USA

A collection of programs are described to analyze and display urodynamic data on a digital plotter. Utilizing a small programmable calculator, routines have been written to characterize the temporal and distributive properties of experimentally observed ureteral peristalses and associated urine output. The encoding principals used are designed to optimally use limited calculator memory. Programmable calculators

Urodynamics

Renal pacemaker

1. I n t r o d u c t i o n Urine is an important biologic fluid providing for the excretion of waste products, the regulation o f body pH, and hydration. Despite these necessary functions, relatively little is known about the physiology of urine transport. Briefly, urine is excreted by the kidney and collected in the renal pelvis (fig. la). From the renal pelvis, it is transported by the ureter to the bladder by peristalsis. The renal pelvis has been shown to possess

URETEROPELVICI~ JUNCTION CLOSED

CEMAKER

URETERAL T MUSCLE / ~LUMEN INTERPERISTALTIC CONTRACTION~ CLOSED INTERVAL

~ :e,~_ PI

a fundamental rhythm due to a pacemaker analogous to the heart. Unlike the heart, however, every beat o f the renal pelvis is not necessarily conducted by the ureter. The exact mechanism of this frequency division at the uretero-pelvic junction is unknown but varies with the level of hydration [1 ]. The elucidation of the factors regulating urine transport has been under active investigation with the dog as an experimental model. During a typical experi. ment, the ureteral electromyogram (EMG), renal pelvic presure, and bolus volume associated with each

RENALPELVIC PRESSURE

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URINE BOLUS

Fig. la. Diagrammatic schema of the experimental model portraying the kidney, renal pelvis, and ureter. A urine bolus is shown in the ureter being propelled by an ureteral peristalsis. Fig. lb. Schematic simplification of the experimental data showing the fundamental pacemaker interval (~), the ureteral EMG with the conducted action potential, and the urine bolus volume being measured via a drop counter.

6

hi.. Silvert, C. Constantinou, Statistical analysis of the temporal and distributive properties ofurodynamic data

ureteral contraction are monitored. The pacemaker frequency is determined from the pressure waveform of the renal pelvis, while the ureteral rate is derived from the ureteral EMG. A typical tracing of these parameters is shown in fig. lb [2]. This communication describes an attempt to evaluate a large amount of data generated while investigating the renal pacemaker. Programs have been written to (1) collect and condense data, (2) characterize graphically the temporal and distributive properties of the urodynamic data, and (3) calculate the statistical properties of the results.

BV 1 , BV 2 , ..., BVn and

(1)

PI1, PI2, " ' , Pin representing the successive bolus volumes and peristaltic intervals respectively. All four of the following programs manipulate these data series in order to achieve their respective analyses. 3.1. Mean f l o w vs. time elapsed

The mean flow (MF) at the ith peristalsis is calculated from

2. Data representation and collection The experimental parameters were recorded on a multichannel polygraph. As shown in fig. 1b, the interperistaltic intervals (PI) were determined by measuring the time intervals between successive EMG peaks. The bolus volume (BV) associated with each ureteral contraction was recorded by a drop counter and correlated with the appropriate contraction. After each experiment, up to 100 registers of data are encoded onto magnetic cards for later use in the analytical programs. Each register of data contains a single number with four decimal places; e.g., XXXX. YYYY. The integer portion of the number (XXXX) represents ten times the interperistaltic interval in seconds while the decimal portion (.YYYY) is equivalent to the bolus volume in milliliters.

3. Program description and flowchart Four programs have been written to represent (A) mean urine flow vs. time elapsed, (B) peristaltic interval vs. time elapsed, (C) peristaltic interval histogram, and (D) bolus volume vs peristaltic rate. In each of the programs, the axes and graph labels are first plotted, following which a magnetic card containing up to 100 registers of data is entered into the calculator memory. The memory then contains two series of numbers:

5

~=-s

BVi+ c

MFi- 5

i=-S

(2)

Pl-7'+c

while the elapsed time (ET) is found by i ETi = ~1 PLi.

(3)

A typical plot of mean flow against time is illustrated in fig. 4a. If 0 > i + C > n, the series is-truncated appropriately, causing < 11 values to be used for calculating the mean flow at the beginning and end of each experimental run. To increase the information displayed by the plot of fig. 3, each point is displayed as a vertical line, the length of which represents the bolus volume (BVi). Thus, the graph gives both the mean flow and bolus volume on the vertical axis as a function of time on the horizontal axis. The flowchart of this program is shown in fig. 2a. 3.2. Peristaltic interval vs. time elapsed

The peristaltic interval at the ith peristalsis (PIi) is given as one of the initial data series (eq. (1)). This value is plotted as a vertical line against the elapsed time at the ith peristalsis (ETi) as defined in eq. (3). Fig. 4b illustrates the variation of peristaltic interval against time. This plot accentuates that all the peristaltic intervals are whole number multiples of the fundamental pacemaker interval. It also indicates the temporal organization of peristaltic activity, particularly

M. Silvert, C. Constantinou, Statistical analysis o f the temporal and distributive properties of urodynamic data

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Fig. 3. Flowchart of bolus volume vs. peristaltic rate.

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Fig. 2. This flowchart contains the f'trst three programs. Subsection A: Mean flow vs. time elapsed. Subsection B: Peristaltic interval vs. time elapsed. Subsection C: Histogram o f the peristaltic frequency distribution.

8

M. Silvert, C. Constantinou, Statistical analysis of the temporal and distributive properties of urodynamic data

in cases where the urine output is transiently altered. The flowchart organization of this program is shown in fig. 2b.

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3. 3. Histogram o f the peristaltic frequency distribution

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In this program, the peristaltic interval series is examined in order to plot the percentage of the series that occurs at each possible PI. Thus, a histogram is formed with the frequency distribution on the horizontal axis and the percentage of the total observations on the vertical axis. Due to the small memory available in the calculator, it is not possible to sort all of the peristaltic intervals into a large number o f sorting bins, as could be done on a standard'computer. Instead, the peristaltic interval data series is scanned to determine which points fall into an arbitrarily chosen bin width. After plotting the result, the examining bin is incremented by 0.1 sec and the entire data series is re-examined. Thus, ?/

[Bin m I = ~ [PIi ~ Bin m ] i=1

(4)

where the bin width = 0.1 sec and m = 0 ~ 1000. Since each grouping of peristaltic intervals represents a statistical distribution of a single peristaltic interval, the program identifies the statistical group by testing whether a given bin is occupied or not; i.e., if IBinml < 1.

(5)

When ten successive bins are found to be empty, one second has elapsed since the last occupied bin. Consequently, if all identified bins since the last identified group are considered to form a new entity, a new group separated from its own members by < 1 sec and from other groups by > 1 sec has been identified. The calculator then calculates and plots (fig. 4c) the number of members, mean, and standard deviation of the new group. The flowchart for this program is given in fig. 2c 3.4. Bolus volume vs. peristaltic rate The bolus volumes are easily identified from the original series (eq. (1)), while the peristaltic rate is derivable from the peristaltic interval series; i.e.,

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Fig. 4. Typical graphical representation of a dog after receiving an intravenous fluid load of 25 ml of 25% mannitol. The upper plot represents mean flow vs. time elapsed; the center graph shows the peristaltic interval vs. time elapsed; and the final plot represents the histogram of the peristaltic frequency distribution. 1 1 1 P R I ' PR2' "' PRn - P I I ' PI 2 .... ' PI-~"

(6)

As PR i is derived from PI i, it is plotted against BVi on the vertical axis, in addition to being added to one o f 150 registers that have been assigned values from 0 to 15 peristalses per minute. Each of these sorting bins thus brackets 0.1 peristalses per minute. As in previous plots, the memory limitations of the calculator require that each 10 digit storage bin store more information than just the number of PRs that fall within its boundaries. A typical storage register XXYYYYZZZZ stores the number of PRs (N) that fall within its bounds; i.e., n

XX~N=~

i=1

[PR i ~ B i n m ] .

In addition, the sum of the BV and BV 2 are also stored in the following manner:

(7)

M. Silvert, C. Constantinou, Statistical analysis of the temporal and distributive properties of urodynamic data

n

YYYY --> ~BV = ~

64 32

BVi (3 Bin m

INTERPERISATALTIC INTERVAL (se~) 16 8 i

(8)

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(9)

Also, since each bin represents a given peristaltic rate, the sum of the PR and the PR 2 are obtained from PR = N IBinml

0.1

~, 0.05 o 2 4 6 8 10 12 14 PERISTALTIC RATE (contractions per minute)

PR 2 = N iBinm t2.

(11)

In this way, each storage bin effectively stores five pieces of data (N, BV, BV 2, PR, and PR 2) that will enable calculation of the means and standard deviations in the following manner: ~BV N

(12)

so of v:i i v PR=

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(10)

and

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Fig. 5. "Cluster" analysis of the bolus volume vs. peristaltic rate data froth the same experiment as in fig. 4.

4. Sample runs The examples displayed in fig. 3a, 3b, 3c and 4 are from a dog that received an intravenous fluid load of 25 ml of 25% mannito to force an active diuretic response. Fig. 4 shows the results of programs A, B, and C, while fig. 5 portrays program D.

(14) 5. Discussion

S.D. of PR = ( ~ _ 1 1 ~ p R 2 - N { ~ }

2 1 ) ]/2 (15)

Visual inspection of the plotted values (shown in fig. 5) reveals that the data points tend to "cluster". This is due to the effect of the fundamental pacemaker frequency. In an attempt to quantify this qualitative observation, the program tests for empty bins around the occupied bins. Whenever a group of occupied bins that are separated from each other by < 10 bins and from other groups by > 10 empty bins is found, the group isidentified as a "cluster". The respective N, ]~BV, ~BV 2, Y.PR, and ]~PR2 of the "cluster" is pooled in order that a mean and standard deviation can be calculated, as in eq. (12)-(15). The mean and standard deviation of each "cluster" is then plotted, as shown in fig. 5. A flow chart of this program comprises fig. 3.

The object of this communication has been to describe four programs utilizing a programmable calculator that allowed characterization of the temporal and distributive properties of a large amount of experimentally observed urodynamic data. The graphical results as presented are easily interpretable by both urologists and physiologists. As shown in the sample runs, the fundamental physiologic process of urine transport from the renal pelvis can be described as a frequency rriodulation of the ureteral action potential from the primary pacemaker rate [3]. Thus, with the aid of a programmable calculator it has been made possible to substantially substitute the computing and plotting capacity of a full scale computer.

10

M. Silvert, C. Constantinou, Statistical analysis o f the temporal and distributive properties o f urodynamic data

6. Mode of availability

Acknowledgement

Details of the programs may be obtained from the authors, Stanford University Division of Urology, Stanford, California 94305, USA.

Partially supported by NIH Training Grant No. T01 AM05513.

References 7. Hardware and software specifications A Hewlett-Packard 9820A programmable calculator with extended memory and a 9862A digital plotter were used in this paper. The language used is an algebraic language hard wired into the calculator.

[1] C.E. Constantinou, Amer. J. Physiol. 226 (1974) 1413. [2] C.E. Constantinou, J.J. Granato and. D.E. Govan, Urol. Int. 29 (1974) 249. [3] M.A. Silvert, J.R. Hrynczuk and C.E. Constantinou, Rhythmicities in the renal and urinary collecting system, in: San Diego Biomed. Symp. (1975).