Use of the Hagen-Poiseuille Law: A New Mathematical Approach for the Integration and Evaluation of Anorectal Physiological Testing in Patients with Faecal Incontinence and Pelvic Dyschezia and in Normal Controls

Abstract

This work was done in order to study the possibility of using the Hagen-Poiseuille law for flow of fluids through tubes to integrate and quantitate the anorectal physiological parameters in patients suffering from faecal incontinence and functional pelvic outlet obstruction compared to normal controls. The Hagen-Poiseuille law was intended to be used in the explanation of the role played by different sensory and motor functions of the anorectal segment in maintaining continence and normal rectal evacuation. The intrarectal pressures during rest, coughing, attempted defaecation, rectal sensation, and rectal compliance at the point of first rectal sensation were measured using anorectal manometry. Anal canal length and diameter were measured using lateral defaecographic views during rest, squeeze, and attempted defaecation, and the anal sphincteric reflex contraction in response to coughing or Valsalva’s manoeuver was measured using plug or needle electromyography. These factors were analyzed using the Hagen-Poiseuille law in order to determine anal canal resistance and flow to air, water, and BaSO₄ during rest, coughing, and attempted defaecation in controls, during attempted defaecation in patients with functional pelvic outlet obstruction, and during rest and coughing in patients with faecal incontinence. The Hagen-Poiseuille law could detect anal continence in all controls and could also detect and quantitate functional pelvic dyschezia in all patients. The equation could detect and quantitate faecal incontinence in 8 of 14 patients (57.14%) during rest, in 11 of 14 (78.57%) during coughing, and in all 14 patients after correction for sensory and reflex deficits. Both the Hagen-Poiseuille law and the law of Laplace and their proposed hybrid law were successful in explaining some facts concerning factors affecting normal continence and defaecation. The Hagen-Poiseuille law is a useful new mathematical approach for the integration and quantitation of normal and abnormal continence and defaecation. It can be used to plan for treatment and to determine the outcome of patients suffering from functional anorectal disease.