Comparison of mathematical methods for calculating colonic compliance in humans: power exponential, computer-based and manual linear interpolation models

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, computer-based and manual linear interpolation. Data were compared and concordance evaluated. Pr50 and Pr90 were not significantly different by all methods for baseline and post-treatment. Respectively, concordance correlation coefficients were: pretreatment, 0.879, 0.464 and post-treatment, 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 post-treatment = 0.322. There were no gender differences in compliance measurements. Results of compliance are highly concordant amongst all models. However, computer-based or manual interpolations appear superior to power exponential models for estimating Pr10.

Figure 1

(A) Example of manual linear interpolation for Pr50. In this approach, a slope was drawn at the 50% of maximum volume points of the (proportionate) volume vs pressure compliance curve. A ruler was then used to identify the intersection of the horizontal line at each (proportionate) volume with the corresponding slope. A vertical line at this intersection was drawn to the x-axis to obtain the interpolated pressure value. (B) Example of manual linear interpolation for Pr10. During the manual linear and computer-based 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 using a ruler.

Figure 2

Example of a compliance curve (the volume response to an imposed pressure) in the colon. The `ideal' curve is generated using this power exponential model. Overall, it has a sigmoidal shape. Note the initial flattening of the line in which an increase in pressure does not cause any change in volume, in contrast to the actual data curve. The second part of the curve is more linear and reflects the elasticity of the colon.

Figure 3

Hypothetical compliance curves associated with an incomplete analysis due to patient intolerance of pain during ascending method of limits. Note that the Pr10 still appraises the shift of the curve and is less inaccurate than Pr50 when the compliance curve is incomplete. Note also that, in all situations, the slope is similar, but it fails to identify the curve's shift to the right.