Abstract
 Top of page
 Abstract
 Background
 Materials and methods
 Results
 Discussion
 Acknowledgment
 References
Abstract Measuring compliance allows differentiation of sensory changes from changes in thresholds because of altered compliance. As compliance of the colorectum is sigmoidal, a power exponential analysis was recommended. We aimed to develop and validate simpler measurements of compliance. Forty subjects (23 female, 17 male) underwent colonic barostat procedures comparing dronabinol vs placebo. Results of the effects on compliance were reported elsewhere. Compliance was determined as volume response to pressures ranging from 0 to 36 mmHg. Pressures corresponding to 10%, 50% and 90% (Pr10, Pr50 and Pr90) of maximum volume at 36 mmHg were estimated using a power exponential model, computerbased and manual linear interpolation. Data were compared and concordance evaluated. Pr50 and Pr90 were not significantly different by all methods for baseline and posttreatment. Respectively, concordance correlation coefficients were: pretreatment, 0.879, 0.464 and posttreatment, 0.879, 0.623. There is larger variation in Pr10 comparing all methods and manual calculations allow for the closest fit to the data. Concordance correlation coefficients were pretreatment = 0.189 and posttreatment = 0.322. There were no gender differences in compliance measurements. Results of compliance are highly concordant amongst all models. However, computerbased or manual interpolations appear superior to power exponential models for estimating Pr10.
Background
 Top of page
 Abstract
 Background
 Materials and methods
 Results
 Discussion
 Acknowledgment
 References
Standardized distensions of viscera utilizing a barostat have been used over the last 2 decades to evaluate colorectal sensorimotor function in health and disease. Compliance of hollow viscera can be described as the ability of the organ to expand (volume change) in response to pressure. In distension studies, compliance is described using the pressure–volume relationship. This is typically achieved using a barostat, which is able to maintain a constant pressure within an airfilled bag that is placed with the lumen and is distended to maintain apposition between the bag and the mucosa of the viscus.^{1}
The barostat is designed to maintain a constant pressure within the bag when the organ contracts or relaxes. To maintain a constant pressure, the volume entering the bag is altered by a servomechanism in the barostat, and the volume is indirectly associated with the tone of the colon or with phasic contractions superimposed on the baseline tone, as observed in health or disease or in response to pharmacological modulation.^{2–4} A plot of volume against pressure (the fixed parameter on the xaxis) reflects viscus compliance, and is measured by the slope of the pressure volume curve.^{5} In barostat studies of viscus sensorimotor function, it is essential to know whether there is a difference in compliance to interpret whether a difference in sensation results from an alteration in the viscoelastic or motor properties of the viscus, or a change in afferent function.^{6} One of the currently accepted methods to measure compliance uses a power exponential model of the volume response to imposed pressure.^{7} The rationale for using a power exponential model is that pressure–volume relationships in the colorectum are sigmoidal. This estimate of compliance is summarized as the pressure observed at half the maximum observed volume (Pr½) where a smaller Pr½ corresponds to a higher compliance. However, given the complexity of the calculation, few centres have adopted the method.
Therefore, our aim was to develop and validate alternative, simpler mathematical measurements of colonic compliance.
Results
 Top of page
 Abstract
 Background
 Materials and methods
 Results
 Discussion
 Acknowledgment
 References
The results of all three methods of calculation of compliance pre and posttreatment are presented in Table 1. Data are presented for the entire group (n = 40) and separately for females (n = 23) and males (n = 17). There are no differences in colonic compliance by gender. Concordance correlation coefficients (CCC; with 95% confidence intervals) pretreatment amongst all three models Pr10, Pr50 and Pr90, respectively, were 0.189 (0.098, 0.278), 0.879 (0.815, 0.922) and 0.464 (0.320, 0.586). The overall CCC (with confidence intervals) posttreatment amongst all three models Pr10, Pr50 and Pr90, respectively, were 0.322 (0.188, 0.444), 0.879 (0.815, 0.922) and 0.623 (0.489, 0.729).
Table 1. Comparison of compliance using power exponential, computerbased linear interpolation and manual linear interpolation models  Exponential model  Computer interpolation  Manual interpolation 

Baseline  PostRx  Baseline  PostRx  Baseline  PostRx 


Pr10*  8.0 and 12.6 [10.2 (1.9)]  6.1 and 12.3 [8.9 (2.4)]  4.9 and 9.2 [6.5 (1.3)]  4.3 and 8.0 [5.9 (1.4)]  4.9 and 7.9 [6.1 (1.4)]  1.3 and 8.0 [5.3 (2.3)] 
Pr50*  15.0 and 22.1 [18.5 (3.1)]  11.4 and 20.4 [16.2 (3.5)]  15.0 and 25.4 [20.6 (4.3)]  11.7 and 23.1 [18.0 (4.4)]  15.3 and 25.3 [20.3 (4.0)]  11.7 and 22.2 [17.6 (4.3)] 
Pr90*  35.2 and 57.0 [47.7 (10.9)]  27.7 and 50.9 [42.0 (9.3)]  27.9 and 41.8 [37.3 (5.7)]  25.0 and 39.7 [34.8 (5.9)]  27.3 and 41.3 [36.9 (5.8)]  23.7 and 39.4 [34.1 (5.9)] 
Females [n = 23 ; mean (SD)] 
Pr10  9.6 (1.7)  8.2 (2.3)  6.2 (1.4)  5.5 (1.4)  6.0 (1.4)  4.7 (2.5) 
Pr50  17.7 (3.2)  15.4 (3.9)  19.6 (4.4)  17.1 (5.1)  19.2 (4.2)  16.8 (5.0) 
Pr90  46.9 (12.9)  41.8 (10.9)  36.7 (6.4)  34.3 (6.8)  36.3 (6.5)  33.5 (6.9) 
Males [n = 17 ; mean (SD)] 
Pr10  10.9 (2.0)  9.8 (1.9)  7.1 (1.0)  6.4 (1.3)  6.2 (1.3)  6.0 (2.0) 
Pr50  19.5 (2.8)  17.3 (2.6)  21.9 (3.8)  19.1 (3.0)  21.8 (3.4)  18.8 (2.7) 
Pr90  48.9 (7.7)  42.2 (6.8)  38.1 (4.7)  35.4 (4.6)  37.7 (4.7)  34.9 (4.9) 
Concordance correlation coefficients between two models are each listed in Table 2. Note that Pr50 and Pr90 values are very similar by all methods of analysis at baseline and posttreatment (Rx) for all three methods. However, there is larger variation in estimates of Pr10. Whereas the computerbased linear interpolation and manual linear interpolation model were highly concordant, both had substantially worse concordance with the power exponential model estimates of Pr10. Moreover, as illustrated in Fig. 2, the fit of the power exponential curve to the actual data in the part of the compliance curve corresponding to low imposed pressures was suboptimal.
Table 2. Concordance correlation coefficients (CCC) comparing power exponential, computerbased linear interpolation and manual linear interpolation models  Power exponential model  Computerbased linear interpolation  Manual linear interpolation 


Pr10 
Power exponential model  –  PostRx – 0.297 (0.159–0.424)  PostRx – 0.251 (0.107–0.384) 
Computerbased linear interpolation  PreRx – 0.178 (0.080–0.274)  –  PostRx – 0.583 (0.349–0.749) 
Manual linear interpolation  PreRx – 0.108 (0.024–0.191)  PreRx – 0.707 (0.522–0.828)  – 
Pr50 
Power exponential model  –  PostRx – 0.866 (0.783–0.918)  PostRx – 0.892 (0.820–0.937) 
Computerbased linear interpolation  PreRx – 0.808 (0.702–0.879)  –  PostRx – 0.989 (0.980, 0.994) 
Manual linear interpolation  PreRx – 0.835 (0.741–0.898)  PreRx – 0.983 (0.968–0.994)  – 
Pr90 
Power exponential model  –  PostRx – 0.579 (0.416–0.707)  PostRx – 0.527 (0.361–0.660) 
Computerbased linear interpolation  PreRx – 0.405 (0.236–0.550)  –  PostRx – 0.978 (0.960–0.988) 
Manual linear interpolation  PreRx – 0.391 (0.225–0.535)  PreRx – 0.991 (0.984–0.995)  – 
Discussion
 Top of page
 Abstract
 Background
 Materials and methods
 Results
 Discussion
 Acknowledgment
 References
In this study, we wished to validate two easier methods of calculating compliance (computerbased linear interpolation and manual linear interpolation) by comparing the results with these approaches to those determined with the power exponential model (standard approach used in our laboratory to date). We have been able to demonstrate that the Pr50 and Pr90 are very similar for all models. We also determined that the manual approach is as accurate as the more sophisticated models for estimating Pr50 and Pr90. In addition, the Pr10, Pr50 and Pr90 values are very similar for the computerbased linear interpolation and manual linear interpolation. Differences observed in estimates of Pr10 between these two linear (computer and manual) models and the power exponential model may reflect the poor fit of the more sophisticated power exponential model to the actual data, as illustrated in Fig. 2. The approach using power exponential analysis provides estimates of the whole compliance curve from the data available for each subject, thereby allowing derivation of an average curve for each treatment or group (based on the constants β and κ of individual curves). Thus, one can estimate differences on the whole curve for different groups or treatments. Linear interpolation approach does not allow the whole curve to be evaluated, but it may allow more accurate estimates of discrete points on the curves.
The current study demonstrates that it is possible to calculate compliance by plotting volume against pressure and manually calculating the slope or more simply estimating the pressures corresponding to specified volumes, such as those at 10%, 50% and 90% of maximum. If this simpler method is adopted more broadly, we believe that this will facilitate reporting of compliance and standardize the observations on viscus compliance across centres. If the manual linear interpolation or computerbased linear interpolation are not used to calculate Pr10, our data suggest that further revision of the power exponential model would be necessary to enhance the ‘fit’ of the exponential curve to the actual data.
A weakness in the study is the inability to determine which model most accurately characterizes Pr10. There are very few actual volume data at the lower levels of imposed pressures. During the manual linear and computerbased linear interpolations, the Pr10 was determined by extrapolating the slope line back from the observed data to the point that traversed the line of the 10% maximum volume (see Fig. 1B). Hence, there may be a potential for minor error. However, as was mentioned previously, the power exponential curve does not exactly fit the data well either, so it is unclear whether the Pr10 value obtained using this model is also inaccurate. It appears that the goodnessoffit of the curve drawn by the power exponential model shows the worst fit in this part of the curve. It is very relevant to define this part of the compliance curve as accurately as possible, because many drugs such as clonidine^{10} and pregabalin^{11} have a significant effect on this section of the compliance curve. This pressure–volume relationship is shifted to the left, whereas the slope of the linear part of the curve is unaffected by the drug being studied, e.g. clonidine.^{10}
It is also important to emphasize that our analysis to date has been based on results in healthy volunteers and further validation in patients would be valuable. This is especially relevant for conditions like irritable bowel syndrome in which hypersensitivity may lead to the participant signalling a level of pain that precludes completion of the planned ascending method of limits to 48 mmHg. The plateau phase of the sigmoidal P : V curve may not be reached in a hypersensitive or hypervigilant patient. Thus, using the 10th, 50th and 90th percentiles of the maximum volume to estimate compliance may present a significant problem in patients who have visceral sensitivity, as in irritable bowel syndrome. In these cases, volume determinations at specific pressures may be a better approach (which has been termed static compliance in prior reports), at least for the pressures that can be achieved during the distensions. It may be argued that, in the absence of a change in the slope of the compliance curve, such a shift in the volume at specific pressures may represent a change in compliance. Such a measurement may also serve as the primary end point in the comparisons of the effects of disease or perturbations such as medications.
However, this concern regarding the pressures achievable during a sequence of distensions is a general criticism for any estimation of compliance: for example, the less steep, uppermost part of the sigmoidal curve may be excluded from the approach that uses a ‘tangent’ or linear interpolation of the plot if the higher pressures are not assessed. In such cases where the compliance curve would be incomplete, the Pr10 becomes a more useful measurement than the Pr50 or Pr90 or of the slope calculation, as it would be able to reflect a shift of the compliance curve to the left or right (Fig. 3). Further validation studies comparing these approaches are required to determine which approach (static compliance or volume at specified pressure vs Pr10 and Pr50) best identify the effects of disease or pharmacological perturbations.
In conclusion, our data suggest that, if it is to be used, the power exponential model needs to estimate Pr10 more accurately. On the other hand, we confirm that the power exponential model provides a good summary for the whole curve. The linear interpolation models yield accurate estimates of pressures at specific percentiles of the maximum volumes observed. We conclude that the manual approach is sufficiently accurate, and would be enhanced by having more data plotted at low pressures. We recommend using pressure increments of 2 mmHg between 0 and 12 mmHg, followed by 4 mmHg increments between 12 and 36 mmHg. This will increase the accuracy for estimating Pr10. The remainder of the compliance calculation is virtually equal using the power exponential, computerbased or manual linear interpolation of the data. Nevertheless, it is important to continue validating these approaches and estimates of static compliance in patients with hypersensitivity or hypervigilance in whom it may not be possible to obtain a full, sigmoidal compliance curve.