Investigating the relationships between peristaltic contraction and fluid transport in the human colon using Smoothed Particle Hydrodynamics
Introduction
The gastrointestinal tract comprises of several distinct organs in sequence, extending over 7 m in the human abdomen. Controlled propulsion and mixing of content along the digestive tract is essential for a normal life. This is achieved by a rich assortment of motor patterns that ensure that movements and propulsion are appropriate for the breakdown of food, absorption of nutrients and excretion of waste. These movements (motility) are due to coordinated contractions and relaxations of circular and longitudinal smooth muscle layers. In terms of quantitative descriptions, gut motility is one of the most complex functions in the body and when abnormalities occur there can be serious consequences. At times there are obvious causes for these abnormalities, for example tumors can impair flow and their surgical and/or radiation treatment can cause damage to the surrounding tissue, muscle and nerves with further implications for modified transport. There are, however, a host of other gastrointestinal abnormalities where the cause of abnormal intestinal transport is less clear. These functional gastrointestinal disorders (FGID) include dysphagia (difficulty in swallowing), fecal incontinence and constipation. While these are generally not life threatening they can be chronic conditions that cause major economic and social burdens because of their prevalence in society and their dramatic impact upon quality of life. In Australia around one third of the population has one or more FGID and 60% of these will seek medical attention [1].
For esophageal FGIDs the combined technical advances in recording abnormal contractility, via esophageal manometry, and relating these abnormalities to impaired flow [2] has seen a dramatic improvement in our understanding of the problem and therefore our ability to treat the patient. However, this is not the case for FGIDs in regions below the stomach. The small and large intestines are relatively inaccessible and obtaining detailed manometric recordings and visualizing the movement of digesta is difficult. As a result our understanding of normal pressure/flow relationships is still relatively simplistic [3]. Therefore while abnormal contractility is implicated in FGIDs [4], [5], [6], how these abnormalities relate to impaired flow remains largely unknown.
Computational modeling of gastrointestinal systems has the potential to help understand these complex relationships. Many mathematical models of peristaltic pumping in flexible tubes have been developed over the last decades and the reader is referred to [7], [8] for comprehensive reviews of this research. The vast majority of these models do not take into account the solid wall mechanics of the flexible tube in predicting the transient wall deformation. Instead the wall shape is fully prescribed. Some exceptions to this include Carew and Pedley [9] who developed a model of peristaltic flow in the ureter with an active contracting wall coupled to the internal resistance from the intra-luminal pressures in an infinitely long tube. Such models are based on lubrication theory and are therefore limited to simple geometry systems with low inertial flows and long waves. They are well suited to studying the dynamics of the ureter. However, the development of intestinal flow models for studying the effect of single and multiple wave trains on transport requires an active wall model that can accommodate more realistic geometry and non-linear wall mechanics.
More recently detailed computational models of esophageal motility [10], [11] have helped to define relationships between motility and flow. In addition CFD models have started to consider the effect of peristaltic motor patterns in the small intestine [12] and the stomach [13], [14]. While these studies in the stomach and small bowel have sourced anatomically accurate wall geometries from MRI, they have not attempted a 2-way coupling of the motor activity in the wall with the fluid content. Instead motor patterns are prescribed as a sequence of fixed geometric changes to the boundary. Physiologically realistic intestinal models need to be able to incorporate a number of factors such as the widely accepted law of the intestine [15], which states that a bolus moves in the digestive tract due to the combined ascending excitatory input upstream causing a contraction coupled with descending inhibitory input or Descending Inhibition (DI) causing the segment of gut immediately ahead of the bolus to relax [16], [17].
We propose a model for the coupled wall flexure and flow dynamics inside the colon subject to peristaltic waves of contraction and relaxation using the Smoothed Particle Hydrodynamics (SPH) method [18], [19]. SPH is a particle-based, transient, Lagrangian method. Computations are performed on a set of SPH ‘particles’, which move with any flow carrying local state information with them. The mesh free nature of SPH means large deformations can be modeled without requiring expensive and diffusive re-meshing. Coupling of fluid/solid motion and wall deformation is therefore captured naturally. These advantages have lead to the modeling of pulsatile blood flow in a carotid artery bifurcation [20] and the prediction of blood flow through a non-pulsatile, axial, heart pump [21].
This colon model consists of a flexible visco-elastic cylindrical tube filled with a viscous fluid. In this initial work the intra-luminal content will be assumed to be Newtonian. The boundary model will incorporate radial contractions of the circular muscle. The addition of the longitudinal contractions of the smooth muscle will be incorporated in a future extension. The model will be used to investigate relationships between wall deformation, intra-luminal pressure and flow. We also explore the role of the DI in generating effective fluid transport. The model will then be used to determine the influence of fecal viscosity, lumen occlusion and length of contraction on transport. This model represents the first step in developing a tool to help us interpret how pressure signals recorded from manometric recordings may relate to the propulsion and mixing of intra-luminal content and how abnormalities in these pressure signals may be associated with impaired flow.
Section snippets
Computational model of colon and traveling peristaltic waves
Smoothed Particle Hydrodynamics (SPH) is a well established numerical method for modeling fluid dynamics. For a detailed introduction to the method, the reader is referred to Monaghan [18]. Here we give a brief summary of the method. A suitable form of the SPH continuity equation gives the evolution of the density ρa of particle a, aswhere va is the velocity and mb is the mass of particle b. The position vector between particles b and a is denoted as rab=ra−rb. The value
Simulation and model parameters
The geometry of the intestinal section is 5 cm in diameter and 30 cm long representing a part of the colon. The elastic stiffness for the wall was 10 N/m and the viscous damping coefficient was 1.9 N s/m. The fecal content for the base case had a density of 1.0 g/cm3 and dynamic viscosity of 1 Pa s.
A simple series of regular waves with 12 s intervals between them is used for this initial study. Each wave commences at the same position near the start of the tube and travels in the antegrade direction at
Development of a single peristaltic wave
We first consider the development of a single peristaltic wave traveling from left to right in a simulation of the base case conditions. The influence of the deforming lumen on the intra-luminal content is apparent in Fig. 2. This shows the development of a single wave of contraction at three times over a period lasting from 1 s before the point of peak contraction/relaxation and up to the point of peak contraction/relaxation. Isosurfaces of longitudinal speed (Fig. 2a) and pressure (Fig. 2b)
Role of descending inhibition
In order to understand the role of the DI in motility we compare the case from the previous section with one where the DI is suppressed (and therefore where there is no relaxation of the circular muscle in advance of the contraction). The pressure and flow field in a vertical plane that passes through the middle of the colon are shown in Fig. 3 for the two cases when the wave form has fully developed. The shaded color represents the fluid pressure with dark blue being low pressure and red being
Effect of viscosity of colonic content
Dewatering of fecal matter during its passage along the colon can produce viscosity variations of orders of magnitude along the length of the colon from fluid-dominated at the start of the colon to semi-solid at the rectum. To better understand the effect of viscosity on the flow and pressure field for a single contraction, we predict coupled flow and bowel wall behavior for the fecal viscosities of 0.01, 0.1, 1 (the base case), 3.0 and 10 Pa s. All other conditions are kept the same as for the
Conclusions
This study introduces a new computational model for the coupled wall flexure and flow dynamics inside the colon subject to peristaltic waves of contraction and relaxation. The SPH method was used to describe the flow of intra-luminal content and the wall deformation was modeled as an active boundary using a visco-elastic spring network where the radial contraction and relaxation of circular muscle arise from changes in muscle tension inside the intestinal walls. Traveling waves were generated
Conflict of interest statement
None declared.
Acknowledgments
Dr. Sinnott, Dr. Cleary and Dr. Arkwright are all supported by funding from CSIRO, Australia. Dr Dinning is supported by NHMRC grant #630502 and the Clinician's Special Purpose Fund of the Flinders Medical Center, Australia. Many thanks to Miss Cyndi Wang through the CSIRO Graduate Fellow program for assistance in prototyping the flow simulations and preliminary visualization.
Dr Matthew D. Sinnott is a Research Scientist at CSIRO Mathematics, Informatics and Statistics, Australia. His research interests include the application of grid-free numerical methods to biological flows using Smoothed Particle Hydrodynamics (SPH), and to industrial granular flows using Discrete Element Method (DEM).
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Dr Matthew D. Sinnott is a Research Scientist at CSIRO Mathematics, Informatics and Statistics, Australia. His research interests include the application of grid-free numerical methods to biological flows using Smoothed Particle Hydrodynamics (SPH), and to industrial granular flows using Discrete Element Method (DEM).
Dr Paul W. Cleary is a Senior Principle Research Scientist at CSIRO Mathematics, Informatics and Statistics, Australia and leader of a Computational Modeling group specializing in particle-based methods. He has been an internationally recognized expert in the development of the numerical methods of Smoothed Particle Hydrodynamics and Discrete Element Method for the last 20 years. He is a member of the editorial boards of Minerals Engineering and International Journal of Mathematics in Industry and has been a Co-Editor of three special journal issues on Computational modelling in the Process industries. His group's research and software technology are well published and considered world leading in many different research application areas, including mining, manufacturing, multiphase flows and geophysical risk.
Dr John W. Arkwright has an extensive background in optical fibre technology and devices, initially for the telecommunications industry and, more recently, for biomedical sensing. He has worked predominantly in industrial R&D from start-ups to multi-national companies, with an emphasis on developing and commercializing new technologies. He has experience at many different levels from fundamental research to production line engineering. He is now a Senior Principle Research Scientist for the CSIRO Division of Materials Science and Engineering, and is leading a team focused on the design, fabrication, and commercialization of fibre-optic catheters for in-vivo diagnostics.
Dr Phil G. Dinning is a Senior Research Fellow in the Department of Human Physiology at Flinders University. He serves on the editorial board of the journals Neurogastroenterology and Motility, and the World Journal of Gastroenterology. For the past 5 years, he has headed up research into colonic functional disorders at the St.George Clinical School at UNSW. He has won national and international awards for his work on colonic motility including the prestigious Gastroenterological Society of Australia Young Investigator Award (clinical division). His research focuses on the measurement of human colonic contractile activity; the development of new tools to map and define the colonic dysmotility associated with severe constipation and faecal incontinence. In addition, he has been instrumental in the development of the novel applications of fibre-optic sensing technology and computational modeling to better understand normal and disordered gut motility.