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Keywords:

  • Automated analysis;
  • colon;
  • manometry

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Funding
  8. Disclosure
  9. Author contributions
  10. References
  11. Appendices

Background  Manual analysis of data acquired from manometric studies of colonic motility is laborious, subject to laboratory bias and not specific enough to differentiate all patients from control subjects. Utilizing a cross-correlation technique, we have developed an automated analysis technique that can reliably differentiate the motor patterns of patients with slow transit constipation (STC) from those recorded in healthy controls.

Methods  Pancolonic manometric data were recorded from 17 patients with STC and 14 healthy controls. The automated analysis involved calculation of an indicator value derived from cross-correlations calculated between adjacent recording sites in a manometric trace. The automated technique was conducted on blinded real data sets (observed) and then to determine the likelihood of positive indicator values occurring by chance, the channel number within each individual data set were randomized (expected) and reanalyzed.

Key Results  In controls, the observed indicator value (3.2 ± 1.4) was significantly greater than that predicted by chance (0.8 ± 1.5; < 0.0001). In patients, the observed indicator value (−2.7 ± 1.8) did not differ from that predicted by chance (−3.5 ± 1.6; = 0.1). The indicator value for controls differed significantly from that of patients (< 0.0001), with all individual patients falling outside of the range of indicator values for controls.

Conclusions & Inferences  Automated analysis of colonic manometry data using cross-correlation separated all patients from controls. This automated technique indicates that the contractile motor patterns in STC patients differ from those recorded in healthy controls. The analytical technique may represent a means for defining subtypes of constipation.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Funding
  8. Disclosure
  9. Author contributions
  10. References
  11. Appendices

A number of techniques are used to investigate colonic motility; however, only one technique that of pancolonic manometry,1 allows us to define motility patterns in real time from multiple sites simultaneously throughout the large bowel. Manometric studies in patients with slow transit constipation have demonstrated differences in contractile activity in comparison to healthy controls,2–9 but as yet there are no contractile patterns that can reliably distinguish all individual patients from healthy control subjects.10,11 Nevertheless, other studies utilizing scintigraphic, radiographic, and telemetric capsule techniques have likewise shown that disturbed motility exists in patients with slow transit constipation.12–14

If such differences in motility indeed exist, then why do we have so much trouble identifying patient-specific manometric abnormalities? This is almost certainly due, to some extent, to the manner in which we analyze the manometric trace. For the most part, recordings are manually scanned to look for propagating pressure waves and then note their frequency, amplitude, velocity, and extent of propagation. This can be problematic because the identification of these events is subject to bias,15 and the spatial resolution between recording sites.16 Alternatively, we can compare traces between groups using the more generic calculations of area under the pressure curve (AUC) or motility index (MI). However, the nonspecific nature of this approach simply means that we can only conclude that there is either more or less colonic ‘activity’ in one group compared to another.

Neither approach examines the potential relationships that exist between propagating events throughout the colon. Coordinated patterns of motility are likely to be a feature of normal motility. We have shown manometric evidence of this through the development of novel graphical17 and analytical techniques.5,18 However, our mapping and analysis are both based upon manually identified propagating sequences.

Automated analysis of colonic motility data could potentially aid our ability to differentiate aberrant colonic contractility in patients from that of healthy controls. However, if the automated approach is based upon pattern-recognition algorithms, which in turn are based on our own preconceived ideas of what a propagating event is, then the output will simply match our visual attempts.19 Another approach published recently, utilized independent component analysis, which attempts to separate noise from genuine motility patterns, and then classify categories of rhythmic events.20 Based on manometric recordings from the distal colon only, this technique successfully separated constipated patients from controls. However, the time–frequency parameters for separating subjects were defined manually, and the classification itself was also done manually.

In this study, we set out to design an entirely automated approach that does not require any form of manual identification. Utilizing time-lagged cross-correlation21 between adjacent recording channels to capture the amount of localized asynchronous coordination, we have developed an automated technique for the analysis of colonic manometric studies. We hypothesized that this technique will differentiate patients with slow transit constipation from healthy controls, independent of pattern-recognition software, which is reliant upon human preconception.

Materials and methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Funding
  8. Disclosure
  9. Author contributions
  10. References
  11. Appendices

We analyzed colonic manometric data acquired from 17 patients with slow transit constipation (STC: mean age: 46 ± 18) and 14 healthy controls subjects (HC: mean age: 30 ± 7). All subjects had been involved in studies published previously.5,18,22 All participants had given written, informed consent and the studies were approved of in Australia by the Human Ethics Committees of the South Eastern Area Health Service, Sydney and the University of New South Wales (05/122), and in London by the Redbridge & Waltham Forest Local Research Ethics Committee (07/H0701/71).

Patient selection criteria

Inclusion criteria have been discussed in detail previously.5,18,22 To minimize subject variability, all patients had scintigraphically confirmed STC23 and normal anorectal manometry, with no evidence of paradoxical sphincter contraction or an inability to expel a rectal balloon.

Healthy controls

All healthy control subjects had a normal bowel habit, defined as between three bowel movements a day and one bowel movement every 3 days, with no symptoms of rectal evacuatory difficulty or any other gastrointestinal symptoms. None had a history of metabolic, neurogenic or endocrine disorder(s) known to cause constipation, they were not taking regular medications (including laxatives), and none had any history of prior abdominal surgery, other than appendicectomy. Pregnancy was excluded in all subjects prior to enrolment by urinary HCG testing. Studies were not performed in any particular phase of the menstrual period.

Manometric catheter characteristics and placement techniques

Data included in these analyses were collated from two different techniques: nasocolonic placement into an unprepared colon (3 patients and 6 controls) and colonoscopic placement into a prepared colon (14 patients and 8 controls). The details of these placement techniques have been described previously.5,22 We have also shown previously that the overall frequency of propagating sequences identified by either technique does not differ.24

Data were selected from the first 4 h of each study, which did not include a meal response. High calorie meals are known to increase colonic contractile activity,3,5 and as the manometric recordings utilized were acquired from studies involving different protocols, it was felt prudent to exclude postprandial data to limit potential variables between the different studies. We also only used studies in which manometric data had been recorded from the entire colon, from cecum to sigmoid/rectum. The identity of each data set was removed, allowing the data to be analyzed in a blinded fashion.

Software development

General overview  The automated approach did not attempt to explicitly identify propagating events. Instead we developed a method that examined the cross-correlation between pressure waves in adjacent channels. A brief overview of the technique is provided below; for specific details, refer to the Appendices.

For each of the blinded data sets, a stepwise approach was employed, involving several elements, which resulted in the calculation of an indicator value. The indicator value is a single number, which essentially provides a gauge of the normality of the colonic contractile patterns within that data set. The first critical step was to remove any baseline drift and synchronous anomalies from each data set (see Appendix 1). The data were then split into 50% overlapping blocks, with each block being 2 min in length (1200 samples at 10 Hz). Then for each channel in each block, the following steps were applied (see also Fig. 1 for a schematic representation):

image

Figure 1.  Algorithm for calculating of the indicator value over a 2-min length block of manometric recording for channel 2 (red line). Fig. 1A shows original data in channels 1–3. These data are then normalized (Fig. 1B) and the cross-correlation between channel 2 and its two adjacent channels (ch 1 & ch 3) is computed in step (1.2) (see Software development: General overview). This results in a cross-correlation wave form of channels 1 and 2 (Fig. 1C) and a separate cross-correlation wave form for channels 2 and 3 (Fig. 1D). Then step (2.1) (see Software development: General overview) calculates the average of these two cross-correlations (Fig. 1E). The negative lags in the average cross-correlation are subtracted from the positive lags (Step 2.2), and the result is squared (Step 2.3). In Fig. 1F the squared-folded cross-correlation wave (green) is shown. The average value of the green line (across the time epoch) is calculated and this averaged squared-folded cross-correlation value is shown as the green hatched line in Fig. 1F.

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  • 1
     For each pair of adjacent channels, within each 2 min block:
  • 1.1
     The area under the curve (AUC) was calculated. To minimize the impact of single large anomalous pressures on the end indicator value, the channel with the larger AUC was normalized to the size of the smaller AUC. This was achieved in the following manner. For each pair of channels (e.g. Channel 1 & 2 in Fig. 1A) a constant was calculated by diving the smaller AUC by the larger AUC. Then each pressure wave within the larger AUC was multiplied by that constant. The normalized data can be seen Fig. 1B.
  • 1.2
     The cross-correlation21 between each pair of channels with normalized data was then calculated. Fig. 1C,D shows the resultant data after calculation of the cross-correlation between channels 1 and 2, and between channels 2 and 3. The relative time separations between the pair of channels, known as lags, were then clipped to a 1 min length, eliminating redundancy in the overlap between blocks.
  • 2
     For each channel with two neighbors, (for example channel 2 in Fig. 1B):
  • 2.1
     The cross-correlations, calculated in step (1.2), were averaged, which resulted in a single representative wave form (Fig. 1E).
  • 2.2
     The averaged cross-correlation was then folded, by subtracting negative lags from the corresponding positive lags. This zeroes any symmetry, where symmetry in the cross-correlation corresponds to synchronous events;
  • 2.3
     Each element in the folded cross-correlations was then squared (see Fig. 1F). This allowed for fewer but larger cross-correlations to have greater efficacy in the final indicator than many smaller cross-correlations. The average value of the squared-folded cross-correlation (green line Fig. 1F) was then calculated. In the example shown (Fig. 1F) the average value of the green line is represented as the hatched green line
  • 3
     Within that 2 min block the same steps were repeated for all other channels with two neighbors. For example if we had 16 channels of data, then we could calculate the averaged squared-folded cross-correlations (hatched green line Fig. 1F) for channels 2–15. In such an example for each 2 min block, across the entire data set, we had 14 averaged squared-folded cross-correlation values calculated. We then took an average of all of these values, which provided us with a single number for that 2 min block across the entire data set.
  • 4
     This entire process was repeated for each overlapping (see General overview above) 2 min time epoch for the entire 4 h recording period. This provided us with a series of averaged squared-folded cross-correlations for each of the 2 min blocks. These individual values were summed to give a single value for the entire 4 h period. As the calculations were based upon 50% overlapping blocks (see General overview above), this effectively doubled the recording length. To deal with this, the final derived value was divided by twice the length of the recording in seconds.
  • 5
     When plotted the attained value for each data set follow a lognormal distribution, with positive-only values on a skewed distribution.25 We then took the natural logarithm of each value, which allowed them to be modeled with a normal distribution, effectively providing us with positive and negative values. Thus, we now had an indicator value for each data set.
  • 6
     The data were then unblinded and based upon these calculated indicator values a decision boundary was created (for calculation of the decision boundary see formulas 6 & 7 in Appendix 2). Indicator values falling on the right hand side of the decision boundary represented ‘normal’ colonic motility, whereas those on the left hand side represented ‘abnormal’ colonic motility.

Classification of an indicator value  As the derived indicator values were based on a relatively small sample size of patients and controls, the next step was to determine the likelihood of any future data set (either patient or control subject) being accurately classified on the basis of an indicator value. To achieve this, a classifier was constructed (see Appendix 2). Using the decision boundary (described in step 6), the classifier calculation determined whether a subject had normal or abnormal colonic motility based on which side of a decision boundary the value fell.

Classifier error prediction  The predictive error of the classifier was then estimated with a cross-validation technique. Leave-one-out cross validation splits the data into two sets: a validation set containing one of the subjects, and a training set containing all of the remaining subjects.26 The classifier is then trained on the training set, and the classification of the validation subject is compared to its known label of normal or abnormal motility. This is repeated such that each subject is in the validation set once. The Bayes error (see Appendix 2 for calculation details) was used as an additional technique for predicting the error of the classifier, based on the modeling the indicator of ‘abnormal’ and ‘normal’ colonic motility with a normal distribution.

Determining the likelihood of indicator values occurring by chance  To determine the likelihood of positive and negative indicator values occurring by chance, the channel numbers within each individual data set were randomized through 100 permutations. Each permutation was then re-analyzed as described above. The average indicator value of the 100 permutations (the expected indicator value) was then compared to the original indicator value (the observed value).

Analysis of distal colonic manometry only  Finally, to match the approach used by Pan et al.20 in which analysis was based upon distal colonic manometry only, the entire analysis was repeated utilizing data acquired from only the descending and sigmoid colon (typically four recording sites). In the randomized data sets (expected data), only 24 permutations were considered (the total number of possible permutations of four channels).

Statistical analysis

The Kolmogorov–Smirnov test was used to compare the observed to expected (randomized) data within patient and control groups, and to compare indicator values between patients and control data. A P value of less than 0.05 was considered to be statistically significant.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Funding
  8. Disclosure
  9. Author contributions
  10. References
  11. Appendices

Indicator value and classification

The classifier of the indicator value (Appendix 2: Equation 7) performed no misclassifications, separating all patients from controls. Cross validation also revealed no misclassifications, and the Bayes error indicated a 97% probability of successfully classifying any additional data set added from future studies.

Analysis of data from pancolonic recordings

In controls, the observed indicator value (3.2 ± 1.4) was significantly greater than that predicted by chance (expected: 0.8 ± 1.5; < 0.0001, Fig. 2), suggesting that there is a coordinated pattern between pressure waves recorded in adjacent channels. By contrast, the observed indicator value in patients (−2.7 ± 1.8) did not differ from the expected data (−3.5 ± 1.6; = 0.1, Fig. 2), suggesting that pressure waves recorded in patients lack the same level of coordination seen in controls.

image

Figure 2.  Plot of the indicator values for each subject. Blue circles represent healthy controls and red circles the patients with slow transit constipation. The associated violin plots35 with each circle show the indicator calculation for 100 random permutations. The black vertical line represents the optimal decision boundary between the two classes. The dark red and blue lines represent the mean indicator values of the patient and control data, respectively, and the light red and light blue lines represent the mean indicator values of the randomized data. In healthy controls, only the observed data differed significantly (P < 0.0001) from the expected data. The mean indicator value in controls also differed significantly from the mean value in patients (P < 0.0001).

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Taken together, the observed indicator values for controls differed significantly to those of patients (< 0.0001), with no overlap between the two groups (Fig. 2). Notably, the observed indicator values obtained from studies where the colon was unprepared did not differ from those obtained from the prepared colon; this was true within either the patient or control groups.

Analysis of data from the distal colon only

In controls, the observed indicator value (1.4 ± 3.6) did not differ from that predicted by chance (expected: −0.1 ± 3.7; = 0.28, Fig. 3). In patients, the observed indicator value (−4.2 ± 2.0) also did not differ from the expected data (−4.8 ± 2.6; = 0.29, Fig. 3). Although the observed indicator values from the control group differed significantly from those of the patient group (= 0.00017), there was overlap between the two, and hence all individual patients could not be separated from controls (Fig. 3).

image

Figure 3.  Plotted indicator values from the distal colon only (four manometry channels). Blue circles represent healthy controls and red circles the patients. The associated violin plots35 with each circle show the indicator calculation for 24 permutations. Unlike the data from the entire colon (Fig. 3), the data from the distal colon were unable to separate all patients from healthy controls with indicator values from both groups falling either side of the black vertical line, representing the optimal decision boundary between the two classes. The dark red and blue lines represent the mean indicator values of the patient and control data, respectively, and the light red and light blue lines represent the mean indicator values of the randomized data.

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Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Funding
  8. Disclosure
  9. Author contributions
  10. References
  11. Appendices

Using a novel automated analytical technique involving cross-correlation for the assessment of manometric recordings of pancolonic motility, this study has shown that all patients with slow transit constipation can successfully be separated from a group of healthy control subjects. This separation was achieved through the analysis of just the first 4 h of recorded data in each study. When the same analysis was applied to data acquired from the distal colon only, the same level of separation could not be achieved.

Although all previous manometric studies comparing colonic motility between patients with constipation and healthy controls have been able to show some significant differences in recorded contractile activities,2–9 no specific contractile patterns have been identified that can be attributed exclusively to either patients or controls.11 This is in contrast to manometric investigation in the esophagus, where specific motor abnormalities are characteristic of specific disorders.27 There are several reasons for this: the esophagus is short and easily accessible and has relatively controlled motility – a patient can be told when to swallow; the motor responses of interest are immediate and short lived (<20 s), and analysis can be performed on well-validated and relatively easily recognized pressure ‘signatures’. In contrast, the colon is much longer, has relatively infrequent propulsive activity that occurs with temporal and regional variations, and no standardized analytical techniques exist.5,15,28

Standardizing the analytical technique can be achieved through automated analysis of the recorded data. Two notable approaches have been attempted. The first of these developed software that attempted to match human visual analysis,19 and although this development was successful, all it really achieved was the detection of events that had already been defined manually, in a faster and arguably more objective fashion. Such an approach, however, is unlikely to define patient-specific motility patterns. More recently, another novel technique was developed,20 which factorized out and hand-selected the most-representative signal of four distal colonic manometry channels via independent component analysis (ICA), and classified each subject into one of three types based on the length and frequency of rhythmic events in that signal by visually inspecting a joint time–frequency plot. Using ICA showed better classification than applying the time–frequency analysis on the original recorded channels. However, the time–frequency parameters for separating subjects were again defined manually and the actual separation of patients from controls also occurred manually.

Our automated approach did not depend upon mimicking visual analysis or upon manual classification of a time–frequency parameter. This allowed the approach to be entirely automated. Based upon the setup of our automated system, the attained indicator values do provide an indication of the motility patterns in patients and controls. Positive indicator values indicate that the motor patterns consist of coordinated, higher amplitude propagated pressure waves. By contrast, negative indicator values are indicative of poorly coordinated, lower amplitude pressure waves.

The negative indicator values in patients are in agreement with early visual observations of colonic motility in constipated subjects. In the 1930s, Kruse performed radiological examination of the constipated colon and observed regions of what he described as ‘overtonicity’.29 This activity lead him to conclude that that constipation was likely to result from incoordination of muscular motor function rather than a simple lack of contractile activity.29 In addition, some of our previous work involving manually analyzed colonic motility recordings has indicated a lack of coordination between sequential colonic propagating events in constipated patients.5,18

An important component of our analysis is that findings were based upon data acquired in the first 4 h of recording. The ability to define motility patterns in a relatively short period of time is of importance for the potential clinical uptake of colonic manometry. Patients, research staff and hospital administrators alike do not appreciate prolonged, overnight studies. While the data utilized in this study were from recordings commencing the day after colonoscopic placement of the catheter, we have since shown that colonic motility is detectable within hours of catheter placement, a fact also confirmed by others.30

Alternatively, although we deliberately excluded a meal response in this study to limit potential confounders, extension of this work could include physiological (e.g. waking or eating) or pharmacological (e.g. Bisacodyl) stimuli within the analysis period, given that constipated patients may have an attenuated response to each.3–9 Such analysis could potentially allow sub-classification of patients into pathophysiological subgroups, to which specific treatments could be targeted.

In contrast to the studies performed by Pan et al.20 we were unable to differentiate all patients from controls on the basis of distal colonic motility alone. Although our technique of cross-correlation examined the relationship between adjacent channels, it did allocate a greater weight to events that extended through greater lengths of the colon. Our group5 and others31 have shown previously in patients with STC, that much of the activity generated in the proximal colon is not transmitted to the distal colon. This is likely to explain why our technique was not as effective when applied to the distal colon only.

In its current form, this automated analysis cannot be applied to data sets that use a different sensor spacing to the data that the classifier was trained on, and retraining may not work for high(er)-resolution recordings without modifying the algorithm to account for the reduction in time lag between events in adjacent channels attributed to the same propagating sequence. Therefore, as we continue to utilize our recently developed high-resolution manometric technique,16 the automated system will require refinement.

In conclusion, although we have been unable to define specific contractile patterns that differentiate patients from controls, collectively, the data yielded throughout the colon over a prolonged period of time does display characteristic and consistent differences. Further studies are still required to determine the worth of this analysis in defining subtypes of constipation. Indeed how our analysis would classify patients with isolated rectal evacuation disorders or patients with ‘normal transit’ constipation remains unknown. We have shown previously that some patients with symptoms of obstructed defecation also display aberrant pancolonic motility,22 and it is likely that these patients would at least be separated from controls. The ability to establish whether slow transit constipation is a primary or secondary phenomenon in patients with a coexistent rectal evacuatory disorder32,33 remains a real challenge, yet is of particular clinical importance in terms of both treating and understanding the disorder. In addition, it is hoped that changes in the indicator value in response to a treatment could provide a biomarker of treatment success.

Funding

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Funding
  8. Disclosure
  9. Author contributions
  10. References
  11. Appendices

PD and LW receive financial support from the National Health and Medical Research Council (ID 630502). PD also receives financial support from the Clinicians Special Purpose Trust Fund of Flinders Medical Centre.

Author contributions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Funding
  8. Disclosure
  9. Author contributions
  10. References
  11. Appendices

PD, SM, and MS collated the data used in this study; PD and LW provided the concept for the study. The software was written by LW. All of the analysis was performed by LW. The paper was written by PD, MS, and LW.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Funding
  8. Disclosure
  9. Author contributions
  10. References
  11. Appendices

Appendices

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Funding
  8. Disclosure
  9. Author contributions
  10. References
  11. Appendices

Appendix 1

Artifact removal

Artifact removal is an essential component of the indicator calculation. As the area under the curve (AUC), calculated via cross-correlation, is the primary contribution to the indicator value, artifact can have a significant effect upon the outcome. Removal of artifact involved the following two steps:

Baseline drift removal

This effectively zeroes inactivity, so that the primary contribution to the cross-correlation comes from isolated-in-time pressure events. The stochastic Bernstein function approximation approach34 is an iterative procedure for calculating the baseline of a signal. We simplified this approach by replacing the Berstein functions with Gaussian functions. As described previously,34 the procedure for removing the baseline is initialized by smoothing the signal array inline image, resulting in inline image. Each iteration follows with the per-sample minimum between b and y being smoothed and stored as b for the next iteration. Finally, the baseline is subtracted from the original signal, and negative values are zeroed. The termination condition for the loop is given by the Eucliden norm of the change in b between iterations crossing a threshold from above: however, we used a fixed iteration count of 10 for better results.

Synchronous anomaly removal

Synchronous anomalies are evident as manometric signals that simultaneously span the entire colon (i.e. a simultaneous event occurring across all manometric channels). To remove these anomalies, the median pressure across all channels is subtracted from each channel, and negative values are zeroed.

Appendix 2

Indicator classification

Given that we know the indicator, x, the probability of a subject’s colonic motility being labeled as either normal or abnormal can then be calculated using Bayes’ theorem:

  • image(1)

where a subject with normal colonic motility is of class = 0 (label inline image), and a subject with abnormal colonic motility is of class = 1 (label inline image). The likelihood of x given a particular labeling is modeled with a Gaussian (normal) distribution

  • image(2)

where μk and σk are the mean and standard deviation of the indicators in the training set for class k. The prior probability for a subject to be a member of class k is given by

  • image(3)

where Nk is the number of members in class k within the training set. The optimal Bayes classifier

  • image(4)

maps the indicator value x to a class label. Since the likelihoods, inline image and inline image, can have different means and standard deviations, then there could be two values of x for which the probability distributions inline image and inline image are equal. We call these decision boundaries, and they represent the values of x that separate the two classes. A sub-optimal, but more robust classifier is used which contains only the decision boundary, θ, between the likelihood means μ1 < θ μ0. This eliminates the cases when an extremely small indicator value could map to the normal motility class, or an extremely large indicator value map to the abnormal motility class.

The value of the decision boundary θ is found by numerically solving for x (bound by the interval μ1 < θ μ0.) the equation

  • image(5)

by using any appropriate optimization algorithm.

The robust classifier is given by:

  • image(6)

The Bayes error is used to calculate the chances of misclassifying a normal subject as abnormal or visa-versa. For the ψ classifier it is given by

  • image(7)