A mathematical model of intestinal oedema formation

Abstract

Intestinal oedema is a medical condition referring to the build-up of excess fluid in the interstitial spaces of the intestinal wall tissue. Intestinal oedema is known to produce a decrease in intestinal transit caused by a decrease in smooth muscle contractility, which can lead to numerous medical problems for the patient. Interstitial volume regulation has thus far been modelled with ordinary differential equations, or with a partial differential equation system where volume changes depend only on the current pressure and not on updated tissue stress. In this work, we present a computational, partial differential equation model of intestinal oedema formation that overcomes the limitations of past work to present a comprehensive model of the phenomenon. This model includes mass and momentum balance equations which give a time evolution of the interstitial pressure, intestinal volume changes and stress. The model also accounts for the spatially varying mechanical properties of the intestinal tissue and the inhomogeneous distribution of fluid-leaking capillaries that create oedema. The intestinal wall is modelled as a multi-layered, deforming, poroelastic medium, and the system of equations is solved using a discontinuous Galerkin method. To validate the model, simulation results are compared with results from four experimental scenarios. A sensitivity analysis is also provided. The model is able to capture the final submucosal interstitial pressure and total fluid volume change for all four experimental cases, and provide further insight into the distribution of these quantities across the intestinal wall.

Experimental evidence and mathematical modeling of thermal effects on human colonic smooth muscle contractility

“…It has been demonstrated that these devices can affect the local temperature of internal colon layers, thus leading to unexpected and undesirable effects similar to POI drawbacks. On this line, in particular, hyperelastic-based models are being studied for applications in medical robotics (20,30), taking into account the internal irregularities of intestinal villi (3), intestinal edema (74), and viscoelasticity (10,67). The effect of temperature may play an interesting role in most of these open problems.…”

A high-order HDG method for the Biot’s consolidation model

“…Biot's seminar work [6][7][8] laid the foundation of the theory of poroelasticity, which models the the interaction between the fluid flow and deformation in an fluid-saturated porous medium. The model is used in several industries such as petroleum and environmental engineering [46,55] and medical applications such as the modeling of the intestinal oedema [54].…”

Error analysis of primal discontinuous Galerkin methods for a mixed formulation of the Biot equations

“…The time-dependent coupling of flow through a porous medium with elastic deformation is referred to as poroelasticity. The modeling of poroelastic deformation is central to applications in a variety of fields including biomechanics [20,24,25], reservoir engineering, and environmental engineering. The poroelasticity equations were first set forth in the work of Terzaghi [21] and Biot [2,3].…”

“…Comprehensive derivations of balance equations for porous media, with constitutive equation assumptions, including those for compressible and incompressible liquids, gasses, multiphase media, linear elastic response, and thermal effects can be found in the literature [1,11]. Direct derivations of Biot's model, from a macroscopic vantage point, are also readily available [13,19,25] in addition to details regarding the existence and uniqueness of weak solutions [19,26].…”

“…In this article a mixed formulation of the mass conservation equation is used, motivated by an application in the biomechanics of intestinal edema [24,25], by introducing the dilation as a primary unknown, in addition to the employment of a pressure dependent source term. This approach differs from the mixed formulations previously mentioned which introduced the flux variable as in [13,14], or the flux and total stress tensor, as in [23].…”