Aliment Pharmacol Ther 2004; 20: 1373–1379.
doi: 10.1111/j.1365-2036.2004.02278.x
Oesophageal pH has a power-law distribution in control and gastro-oesophageal reflux disease subjects J. D. G ARDNER*, S. SLOAN , M. ROBINSONà & P. B. M INER à *Science for Organizations, Inc., Chatham, NJ, USA; Janssen Pharmaceutica Inc., Titusville, NJ, USA; àOklahoma Foundation for Digestive Research, University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA Accepted for publication 10 September 2004
SUMMARY
Background: We are unaware of any solid theoretical or pathophysiological basis for selecting pH 4 or any other pH value to assess oesophageal acid exposure or to define oesophageal reflux episodes. Aim: To examine the frequency of different oesophageal pH values in control and GERD subjects. Methods: Oesophageal pH was measured for 24 h in 57 gastro-oesophageal reflux disease subjects and 26 control subjects. Histograms were constructed using the 21 600 values from each recording and bins of 0.25 pH units.
INTRODUCTION
Oesophageal pH is frequently recorded continuously for 24 h and such recordings generate thousands of values. In most instances, however, these values are collapsed into single summary measures for the entire recording period. A common summary measure of oesophageal acid exposure is the percentage of the recording period that oesophageal pH £ 4.1–6 Other summary measures include the number and duration of oesophageal reflux episodes determined using pH 4 to define the beginning and end of a reflux episode.1–6
Correspondence to: Dr J. D. Gardner, Science for Organizations, Inc., 156 Terrace Drive, Chatham, NJ 07928, USA. E-mail:
[email protected] 2004 Blackwell Publishing Ltd
Results: Compared with controls, gastro-oesophageal reflux disease subjects had significantly more low pH values and significantly fewer high pH values. In both gastro-oesophageal reflux disease and control subjects, the frequency of oesophageal pH values was characterized by a power-law distribution indicating that the same relationship that describes low pH values also describes high pH values, as well as all values in between. Conclusions: The distribution of oesophageal pH values indicates that a variety of different pH values can be used to assess oesophageal acid exposure, but raises important questions regarding how oesophageal reflux episodes are defined.
We are unaware of any solid theoretical or pathophysiological basis for selecting pH 4 or any other oesophageal pH value for these assessments. This is not to say that a particular pH value cannot be used to assess oesophageal acid exposure or define the occurrence of oesophageal reflux episodes, only that there is no clear rationale for selecting a particular pH value. In the present analyses we examined the distributions of oesophageal pH values obtained in two of our previous studies of normal and gastro-oesophageal reflux disease (GERD) subjects.7–9 In particular, we searched for some rationale based on the distribution of oesophageal pH values for using a particular pH value to quantify oesophageal acid exposure or to define oesophageal reflux episodes. For example, if the oesophageal pH data can be described by a Gaussian 1373
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distribution with a mean at pH 4, this might support the selection of pH 4 to define oesophageal acidity and reflux episodes. We found, however, that in control subjects as well as GERD subjects at baseline and during treatment with a proton pump inhibitor (PPI), the distribution of oesophageal pH values can be described by a power-law. This finding indicates that the same relationship that describes low pH values also describes high pH values in normal subjects and GERD subjects. METHODS
The present analyses were based on data obtained in two different studies that have been described in detail previously.9 The study was conducted at the Oklahoma Foundation for Digestive Research on the campus of the University of Oklahoma Health Sciences Center. Control subjects were 26 healthy adults with no history of gastrointestinal disease or symptoms (16 males, 10 females; age 19–53). GERD subjects were 57 adults with a history of GERD who experienced heartburn at least four times per week for at least 6 months (36 males, 23 females; age 18–69). All control and GERD subjects had a negative serology test for Heliobacter pylori. In control subjects, 24-h gastric pH and oesophageal pH were measured on two separate occasions, 7 days apart. In 57 GERD subjects, 24-h gastric pH and oesophageal pH were measured once. Twenty-six of the GERD subjects with oesophageal pH £ 4 for at least 10% of the 24-h baseline recording period were randomized to receive eight consecutive daily doses of 20 mg omeprazole or 20 mg rabeprazole in a crossover fashion with a 14-day washout between treatment periods. Gastric pH and oesophageal pH were measured for 24 h on days 1, 2 and 8 with each treatment. For all pH recordings, subjects fasted from approximately 22:00 hours the evening before until the beginning of pH recording the following morning at 08:00 hours. Standardized meals were provided at breakfast (09:00 hours), lunch (12:00 hours) and dinner (18:00 hours). Smoking and ingestion of food other than the test meals were prohibited during the pH recording periods. Gastric and oesophageal pH values were recorded every 4 s using an ambulatory, dual-channel pH recording system (Medtronic Synectics, Medtronic Synectics, Shoreview, MN, USA) with antimony electrodes. One electrode was placed in the stomach
10 cm below and the second was placed in the oesophagus 5 cm above the manometrically defined upper border of the lower oesophageal sphincter. Electrodes were calibrated to pH 1 and 7 and connected to a portable data storage unit (Digitrapper; Medtronic Synectics). Recordings began at 08:00 hours and continued for 24 h. Data were transferred from the portable data storage unit and processed using software designed for pH recordings (Polygram for Windows; Version 2.04, Medtronic Synectics). The present analyses are based on the 21 600 oesophageal pH values that are obtained in each 24-h recording. A histogram of these values was generated for each recording using bins of 0.25 pH units from pH 1 to 6, and the frequency of values in each bin was expressed as a percentage of the sum of the pH values from pH 1 to 6. As the present analyses were not specified before the studies were actually conducted, we used a recommended statistical approach for analysing sufficiently large databases.10 We first performed analyses using recordings from 28 randomly selected GERD subjects and 13 randomly selected control subjects. These analyses were used to generate hypotheses that were then confirmed by performing the same analyses on the remaining records.10 The results presented in this paper are from all subjects, but were confirmed in the two separate analyses. Statistical analyses were performed using GraphPad for InStat version 3.01 for Windows (GraphPad Software, San Diego, CA, USA). Curve-fitting was performed using GraphPad Prism version 4.00 for Windows (GraphPad Software). RESULTS
Figure 1 is a histogram of oesophageal pH values from controls and GERD subjects. Both graphs have long tails in that they are characterized by a high number of high pH values and progressively smaller number of lower pH values. There is no apparent discontinuity or break at any pH, particularly not at pH 4. These graphs also illustrate a unique feature of the oesophagus, shared only with the stomach and duodenum, in that it is routinely exposed to acid concentrations that vary over 10 000-fold. The graph for control subjects (Figure 1 left) differs from that for GERD subjects (Figure 1 right) in that control subjects have more high pH values and fewer low pH values. This difference is depicted more
2004 Blackwell Publishing Ltd, Aliment Pharmacol Ther 20, 1373–1379
POWER-LAW DISTRIBUTION FOR OESOPHAGEAL PH
GERD
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Frequency GERD minus Control (%)
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Frequency GERD minus Control (%)
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6
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Postprandial Oesophageal pH
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24-Hour Oesophageal pH
2
20
2 0 -2 -4 -6 -8
-12 6
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Frequency GERD minus Control (%)
Figure 1. Histogram of 21 600 values from 24 h oesophageal pH recording. Results are mean values from 52 records in control subjects (left) and 57 gastro-oesophageal reflux disease subjects (right). Each bin is 0.25 pH.
25
Frequency (%)
25
Frequency (%)
Control
1375
-10
Oesophageal pH
Oesophageal pH
Figure 2. Histogram of difference in values for pH from 24 h oesophageal pH recording. Results are means 52 records in 26 control subjects and from 57 gastro-oesophageal reflux disease (GERD) subjects. Each bin is 0.25 pH units. Values were calculated as the mean for GERD subjects minus the corresponding mean value for controls. Post-prandial pH was from 09:00 hours to 22:00 hours and nocturnal pH was from 22:00 hours to 09:00 hours. Closed symbols are significantly different (P < 0.01) by unpaired t-test comparing logarithm of frequencies.
clearly in Figure 2 (left), which plots the difference in frequencies between GERD and control subjects at different pH values. In Figure 2 (left), there is no significant difference between the frequency for controls and that for GERD subjects at pH 5. Compared with controls, GERD subjects have significantly fewer pH values above pH 5 and significantly more pH values below pH 5. Previously,9 we have pointed out important differences between control and GERD subjects with respect to postprandial and nocturnal oesophageal acidity. Figure 2 (middle and left) illustrates that the differences in the distribution of pH values between control and GERD subjects that occur when the entire 24-h pH record is examined are also present during both the post-prandial and the nocturnal periods. It appeared that the distributions illustrated in Figure 1 can be described by a power law.11–13 That is, the frequency of what is being measured is a constant negative exponential function of the magnitude of what is being measured. In other words, the number of events of a given magnitude N(s) is a function of s)c, where s is the magnitude of the event and c is the exponential
constant. (By convention, c is often used for the power-law exponent.) This relationship, N(s) ¼ s)c, is referred to as a ‘power law’ because the number of events is a power of the magnitude of the event. The negative exponent indicates that there will be a relatively large number of events of small magnitude and a relatively small number of events of large magnitude. A convenient way to search for a possible power-law relationship is to plot the logarithm of the number of events [log N(s)] vs. the logarithm of the magnitude of events (log s) and test for a straight line. If a straight line is obtained, the slope of the line will be equal to the power-law exponent c, i.e. log N(s) ¼ )c log s. Figure 3 plots the log of the frequencies of various pH values vs. the pH values themselves for 24-h oesophageal pH recordings as well as for the portions of the recording during the post-prandial and nocturnal periods. As the pH is the negative logarithm of the hydrogen ion concentration, there is no need to transform the values on the X-axis to analyse the data. The straight lines in Figure 3 are the least-squares lines for the points that are graphed. We fit the data for each
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1.6
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Frequency (log %)
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Oesophageal pH
Oesophageal pH
Frequency (log %)
24-Hour Oesophageal pH
Frequency (log %)
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Figure 3. Histogram of logarithm of frequency of values for pH from 24 h oesophageal pH recording. Results are mean values from 52 records in 26 control subjects and 57 gastro-oesophageal reflux disease subjects. Each bin is 0.25 pH units. Post-prandial pH was from 09:00 hours to 22:00 hours and nocturnal pH was from 22:00 hours to 09:00 hours. The solid lines are the least-squares fits of the data, and for each fit, the value of r2 was at least 0.96.
Control (n ¼ 52) GERD (n ¼ 57)
post-prandial period that was higher than that for the nocturnal period indicating more oesophageal acidity during the nocturnal period.
Control
GERD
1.8
1.8
1.6
1.6
Post-prandial exponent
Post-prandial exponent
of the 57-pH recordings from GERD subjects and the 52-pH recordings from controls using a variety of linear and non-linear equations. Except for one record from GERD subjects and three records from control subjects that were best fit by a second-order polynomial, all records were best fit by a straight line indicating that the frequency of oesophageal pH values is characterized by a power-law. Figure 3 also illustrates that for the entire 24-h period as well as the post-prandial and nocturnal periods, the line for GERD subjects had a lower slope than that for control subjects, and Table 1 shows that the power-law exponents for these two groups were highly significantly different. Figure 4 illustrates values for the power-law exponents during the post-prandial and nocturnal periods for control and GERD subjects. Most records had a higher exponent during the nocturnal period than during the post-prandial period indicating less oesophageal acid exposure during nocturnal period (e.g. see Figure 3). On the contrary, three records from control subjects and 17 records from GERD subjects had an exponent for the
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1.4
1.6
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1.6
1.8
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Figure 4. Plots of exponents for the frequency of values for pH from 24 h oesophageal pH recording. Results are from 52 records in 26 control subjects and 57 gastro-oesophageal reflux disease subjects. The exponent was the least-squares slope of a plot of the logarithm of the frequency vs. pH as illustrated in Figure 3. Postprandial pH was from 09:00 hours to 22:00 hours and nocturnal pH was from 22:00 hours to 09:00 hours. The solid diagonal line is the identity line. Values above the identity indicate that the value on the Y-axis is higher than the corresponding value on the X-axis. Values below the identity line indicate the opposite.
24 h
Post-prandial
Nocturnal
0.556 (0.513, 0.598)
0.487 (0.447, 0.527)
0.853 (0.758, 0.948)
0.345 (0.309, 0.380)
0.318 (0.281, 0.355)
0.509 (0.419, 0.599)
Table 1. Values for power-law exponents for oesophageal pH in control and gastrooesophageal reflux disease subjects
Values given are mean (95% CI) and were calculated from the least-squares slope of a plot of the logarithm of the frequency vs. pH. All values for gastro-oesophageal reflux disease (GERD) subjects are significantly different from corresponding values from control subjects (P < 0.0001 by unpaired t-test). For both control and GERD subjects, values for the postprandial period are significantly different from corresponding values for the nocturnal period (P < 0.0001 by paired t-test). 2004 Blackwell Publishing Ltd, Aliment Pharmacol Ther 20, 1373–1379
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Oesophageal pH
Oesophageal pH
Frequency (log%)
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GERD
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Figure 5. Left and middle panels give histogram of 21 600 values from 24 h oesophageal pH recordings. Right panel gives plots of the logarithm of the frequencies given in the left and middle panels. The straight lines are the least-squares fit of the data. Results are mean values from 26 gastro-oesophageal reflux disease subjects at baseline and after 8 days of treatment with omeprazole or rabeprazole. Each bin is 0.25 pH units.
the PPI was 0.556 (0.490, 0.622). The power-law exponent for the data in Figure 5 (left) is significantly lower than that for the data from the GERD subjects in Figure 1, because the GERD subjects in Figure 5 were selected for high oesophageal acidity. Interestingly, the power-law exponent for the data from GERD subjects treated with a PPI (Figure 5) was numerically identical to that for control subjects (Figure 1 and Table 1). Figure 6 displays the effect of the PPI on the distribution of oesophageal pH values during the entire 24-h period as well as during the post-prandial and nocturnal periods. The patterns with the PPI in Figure 6 are clearly different from those for the differences between GERD and control subjects in Figure 2. In Figure 6, during each period, the PPI significantly decreased the percentage of values below pH 4 and the percentage above pH 5.5 and significantly increased the percentage of values from 4.5 to 5.5. The results in Figure 6 also show that using the conventional assessment of time pH £ 4 will attenuate the magnitude of the effect of the PPI on oesophageal acidity. A preferable end point
6
6
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Oesophageal pH
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1
Frequency (%)
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Nocturnal Esophageal pH GERD minus PPI
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6
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24-Hour Esophageal pH GERD minus PPI
4 2 0 -2 -4 -6
Frequency (%)
Figure 5 (left and middle) displays histograms of oesophageal pH values during 24-h recordings in the GERD subjects who were treated with a PPI. The graph of baseline oesophageal pH is similar to that in Figure 1 (right), but the results in Figure 5 are from the subset of 26 GERD subjects with oesophageal pH £ 4 for at least 10% of the 24-h baseline recording period, whereas those in Figure 1 are from all 57 GERD subjects. The graph of values during PPI treatment also has a long tail, but differs from that at baseline in that there are fewer low pH values and high pH values, but more pH values in the range of 4.5–5.5. Figure 5 (right) shows that a plot of the logarithm of the frequency vs. pH could be described by a straight line for GERD subjects at baseline. Although the distribution with a PPI had a maximum at pH 5, the distribution could still be approximated by a power law for values from pH 5 to pH 1. The values of r2 for the solid lines in Figure 5 (right) are 0.964 at baseline and 0.942 with the PPI. The power-law exponent [95% confidence interval (CI)] for the baseline data was 0.246 (0.224, 0.269) and for
-8 -10 6
5
4
3
2
1
Oesophageal pH
Figure 6. Histogram of difference in values for pH from 24 h oesophageal pH recordings. Results are mean values from 26 gastrooesophageal reflux disease (GERD) subjects at baseline and after 8 days of treatment with some prazole or rabeprazole. Each bin is 0.25 pH units. Values were calculated as the mean for GERD subjects at baseline minus the corresponding mean value after 8 days of treatment with a proton pump inhibitor. Post-prandial pH was from 09:00 hours to 22:00 hours and nocturnal pH was from 22:00 hours to 09:00 hours. Closed symbols are significantly different (P < 0.01) by paired t-test comparing logarithm of frequencies. 2004 Blackwell Publishing Ltd, Aliment Pharmacol Ther 20, 1373–1379
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might be the percentage of time oesophageal pH 4.5–5.5, because during a 24-h oesophageal pH recording, the magnitude of the effect of the PPI using this measure is significantly higher than the magnitude of that using time pH £ 4 (P ¼ 0.023 by paired t-test). DISCUSSION
A particular oesophageal pH value, usually pH 4, is often used to distinguish between oesophageal acid exposure in GERD subjects and that in normal subjects.1–6 The present results provide a rationale for using a particular pH value based on the differences between the frequencies of different pH values in GERD and normal subjects. That is, the present results illustrate that a variety of different pH values can be used to distinguish between normal and GERD subjects and that there is nothing special about pH 4. Our present findings can also explain previous results of others who found that different oesophageal pH values of 3.0, 3.5, 4.0, 4.5 and 5.0 were approximately the same in distinguishing between normal and GERD subjects.3 One way to distinguish between normal and GERD subjects without selecting a particular pH value is to calculate integrated oesophageal acidity, which considers all oesophageal pH values without selecting a particular oesophageal pH value as a cut point.7–9 Investigators have also assessed the effect of a PPI on oesophageal acidity using time pH £ 4, but the rationale for this choice is usually not stated.14–16 The present results show that in GERD subjects, the difference between the distributions of oesophageal pH with and without a PPI is clearly not the same as the difference between the distributions of oesophageal pH values in GERD and control subjects. Thus, although time oesophageal pH £ 4 might be suitable for distinguishing between GERD and control subjects, it may be less optimal for assessing the effect of a PPI on oesophageal acidity. The present results provide a solution to this problem by showing that the distribution of oesophageal pH values can provide a clear rationale for using a particular pH value or range of pH values to assess the effect of a PPI on oesophageal acidity. For example, using time oesophageal pH £ 4 can attenuate the magnitude of the measured effect of a PPI, but the attenuation can be avoided by using time oesophageal pH 4.5–5.5. This attenuation may account at least in part for failure to detect differences between effects of different PPI or different dosing regimens on oesophageal acidity.14–16
Many investigators also use pH 4 to identify an oesophageal reflux episode in that the episode is defined as beginning when oesophageal pH £ 4 and ending when pH > 4.1–6 Some, however, have defined a reflux episode as a decrease in oesophageal pH ‡ 1 without specifying what defines the beginning and end of the episode (e.g. Sifrim et al.).17 As is the case for the other uses of pH 4, the basis for these definitions is usually not specified. The present results, which demonstrate a smooth transition from high oesophageal pH values to low pH values, provide no support for using pH 4, any other pH or a change of any particular magnitude to define an oesophageal reflux episode. It may be that oesophageal reflux episodes are associated with a wide range of pH values and are not restricted to those that decrease oesophageal pH to below pH 4 or that produce a decrease of one pH unit. Previously,7 we reported that some GERD subjects have most of their oesophageal acid exposure during the nocturnal period. In the present study we also found that approximately 30% (17 of 57) of GERD subjects had a lower power-law exponent during the nocturnal period than during the post-prandial period, indicating more oesophageal acid exposure during the nocturnal period. In contrast, only 6% (three of 52) of oesophageal pH records from normal subjects showed this relationship. We do not know the basis for this difference in GERD subjects; however, it does indicate that different pathophysiological mechanisms may exist in subsets of GERD subjects. Power-law distributions are often described as being ‘scale-free’, not only because the log-log relationship has no dimensions, but also because the straight line that characterizes the log-log plot has the same slope over all values. There is no curvature, hump or discontinuity to the line. The power-law relationship between frequency and oesophageal pH observed in the present analyses indicates that the same relationship that describes low pH values also describes high pH values, as well as all values in between, although many investigators focus only on values below pH 4. Some situations in which the distribution of events of different magnitudes can be described by power-laws have been interpreted to reflect the presence of a selforganizing critical state or complexity.11–13, 18–21 The critical behaviour results from self-organized interactions among the individual units of the system without any outside organizing force. The interactions are such that they produce results having a wide range of
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magnitudes and the frequency of each magnitude can be described by a power-law. Similarly, the power-law distribution of oesophageal pH values observed in the present study might result from a self-organized critical state or complexity, possibly in the stomach. ACKNOWLEDGEMENTS
This work was supported by grants from Janssen Pharmaceutica Research Foundation to the Oklahoma Foundation for Digestive Research and to Science for Organizations, Inc. REFERENCES 1 Schindlbeck NE, Heinrich C, Konig A, Dendorfer A, Pace F, Muller-Lissner SA. Optimal thresholds, sensitivity, and specificity of long-term pH-metry for detection of gastroesophageal reflux disease. Gastroenterology 1987; 93: 85–90. 2 Wiener GJ, Morgan TM, Copper JB, et al. Ambulatory 24-hour esophageal pH monitoring. Dig Dis Sci 1988; 33: 1127–33. 3 Schindlbeck NE, Ippisch H, Klauser AG, Muller-Lissner SA. Which threshold is best in esophageal pH monitoring? Am J Gastroenterol 1991; 86: 1138–41. 4 Jamieson JR, Stein HJ, DeMeester TR, et al. Ambulatory 24-H esophageal pH monitoring: normal values, optimal thresholds, specificity, sensitivity, and reproducibility. Am J Gastroenterol 1992; 87: 1102–11. 5 Ghillebert G, DeMeyere AM, Janssens J, VanTrappen G. How well can quantitative 24-hour intraesophageal pH monitoring distinguish various degrees of reflux disease? Dig Dis Sci 1995; 40: 1317–24. 6 Dent J. Gastro-oesophageal reflux disease. Digestion 1998; 59: 433–45. 7 Gardner JD, Rodriguez-Stanley S, Robinson M. Integrated acidity and the pathophysiology of GERD. Am J Gastroenterol 2001; 96: 1363–70.
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8 Gardner JD, Perdomo C, Sloan S, et al. Integrated acidity and rabeprazole pharmacology. Aliment Pharmacol Ther 2002; 16: 455–64. 9 Gardner JD, Sloan S, Miner PB Jr, Robinson M. Meal-stimulated gastric acid secretion and integrated gastric acidity in gastro-oesophageal reflux disease. Aliment Pharmacol Ther 2003; 17: 945–53. 10 Motulsky H. Multiple comparisons. In: Intuitive Biostatistics. New York: Oxford University Press, 1995: 118–26. 11 Hunter P. The power of power laws. Scientist 2003; 17: 22–31. 12 Bak P. How Nature Works. New York: Springer-Verlag, 1996. 13 Barabasi A-L. Linked: The New Science of Networks. Cambridge: Persus Publishing, 2002. 14 Klinkenberg EC, Meuwissen SGM. Combined gastric and oesophageal 24-hour pH monitoring and oesophageal manometry in patients with reflux disease, resistant to treatment with omeprazole. Aliment Pharmacol Ther 1990; 4: 485–95. 15 Holloway RH, Dent J, Narielvala F, Mackinnon AM. Relation between oesophageal acid exposure and healing of oesophagitis with omeprazole in patients with severe reflux esophagitis. Gut 1996; 38: 649–54. 16 Kuo B, Castell DO. Optimal dosing of omeprazole 40 mg daily: effects on gastric and esophageal pH and serum gastrin in healthy controls. Am J Gastroenterol 1996; 91: 1532–8. 17 Sifrim D, Holloway R, Silny J, Tack J, Lerut A, Janssens J. Composition of the postprandial refluxate in patients with gastroesophageal reflux disease. Am J Gastroenterol 2001; 96: 647–55. 18 Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’ networks. Nature 1998; 393: 440–2. 19 Jeong H, Tombor B, Albert R, Oltvai ZN, Barabasi A-L. The large-scale organization of metabolic networks. Nature 2000; 407: 651–4. 20 Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabasi A-L. Hierarchical organization of modularity in metabolic networks. Science 2002; 297: 1551–5. 21 Oltvai ZN, Barabasi A-L. Life’s complexity pyramid. Science 2002; 298: 763–4.
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