Effects of gastrointestinal tissue structure on computed dipole vectors

BioMedical Engineering OnLine Effects of gastrointestinal tissue structure on computed dipole vectors Travis M Austin 1 Liren Li 1 Andrew J Pullan 0 1 Leo K Cheng 1 0 Department of Engineering Science, The University of Auckland , Private Bag 92019, Auckland 1142 , New Zealand 1 Bioengineering Institute, The University of Auckland , Private Bag 92019, Auckland 1142 , New Zealand Background: Digestive diseases are difficult to assess without using invasive measurements. Non-invasive measurements of body surface electrical and magnetic activity resulting from underlying gastro-intestinal activity are not widely used, in large due to their difficulty in interpretation. Mathematical modelling of the underlying processes may help provide additional information. When modelling myoelectrical activity, it is common for the electrical field to be represented by equivalent dipole sources. The gastrointestinal system is comprised of alternating layers of smooth muscle (SM) cells and Interstitial Cells of Cajal (ICC). In addition the small intestine has regions of high curvature as the intestine bends back upon itself. To eventually use modelling diagnostically, we must improve our understanding of the effect that intestinal structure has on dipole vector behaviour. Methods: Normal intestine electrical behaviour was simulated on simple geometries using a monodomain formulation. The myoelectrical fields were then represented by their dipole vectors and an examination on the effect of structure was undertaken. The 3D intestine model was compared to a more computationally efficient 1D representation to determine the differences on the resultant dipole vectors. In addition, the conductivity values and the thickness of the different muscle layers were varied in the 3D model and the effects on the dipole vectors were investigated. Results: The dipole vector orientations were largely affected by the curvature and by a transmural gradient in the electrical wavefront caused by the different properties of the SM and ICC layers. This gradient caused the dipoles to be oriented at an angle to the principal direction of electrical propagation. This angle increased when the ratio of the longitudinal and circular muscle was increased or when the the conductivity along and across the layers was increased. The 1D model was able to represent the geometry of the small intestine and successfully captured the propagation of the slow wave down the length of the mesh, however, it was unable to represent transmural diffusion within each layer, meaning the equivalent dipole sources were missing a lateral component and a reduced magnitude when compared to the full 3D models. Conclusion: The structure of the intestinal wall affected the potential gradient through the wall and the orientation and magnitude of the dipole vector. We have seen that the models with a symmetrical wall structure and extreme anisotropic conductivities had similar characteristics in their dipole magnitudes and orientations to the 1D model. If efficient 1D models are used instead of 3D models, then both the differences in magnitude and orientation need to be accounted for. - Background The stomach and small intestine have a common wall structure that consists of alternating layers of smooth muscle (SM) and pacemaker interstitial cells of Cajal (ICCs) [1]. The wall of the small intestine, in particular, is commonly represented by an outer longitudinal muscle (LM) layer and an inner circular muscle (CM) layer. These layers are separated by the myenteric plexus that contains the ICCs. ICCs are also found within the CM layer but their exact role is still uncertain. Two basic patterns of electrical activity are present in the small intestine: slow waves and action potentials [1]. Slow waves are spontaneous rhythmic oscillations of the transmembrane potential. They have been shown to initiate in the ICCs and then conduct to smooth muscle cells via gap junctions [2]. At the peak of a slow wave, action potentials (sometimes referred to as 'spiking activity') can be triggered to generate a contractile response. Slow wave shape, frequency, amplitude and duration vary in different species and in different parts of the GI tract. In the human small intestine, slow wave frequency is around 12 cycles per minute (cpm) in the duodenum and decreases gradually to around 8 cpm at the terminal ileum [3,4]. In this article we only consider slow wave activity in the small intestine with the aim of improving the understanding of motility diseases associated with electrical disorders such as gastroparesis and myoelectrical dysrhythmia [5,6]. Simultaneously there is ongoing research into using Super Quantum Interference Devices (SQUIDs) to non-invasively measure the magnetic field of the small intestine and then use that information to characterise the underlying electrical fields in the intestine [7,8]. To interpret such recordings, however, requires understanding of what a normal magnetic field is in contrast to an abnormal magnetic field. Modelling has the potential to bring significant insight into this problem. Dipoles are commonly used to represent the net electrical activity within a section of tissue or organ [9-12]. However, it is less certain how to relate the different dipole configurations back to the underlying electrical waveforms. This is especially true in the small intestine due to the alternating muscle layers and high regions of curvature. Previous studies have shown that the intestinal dipoles may point at an angle to the intestinal wall rather than down the length of the intestine in the gross direction of the electrical activity [12]. It was postulated that the potential gradient through the intestinal wall was responsible for this behaviour. To help understand this behaviour further, we have explored similar calculations to [12] on a simpler geometry to carefully separate observed solution behaviour into its dependency on potential gradients through the intestinal walls and its dependency on geometric curvature. In this study, we explore the contributing effects of different parameters on the magnitude and orientations of resultant equivalent dipole sources. These simulations have been performed on simplified geometries (a onedimensional structure and a three-dimensional cylinder both with a straight and bent sections) which are topologically similar to short sections of a small intestine. This allowed the effects of curvature on the dipole parameters to be isolated. The effects of 1D and 3D meshes and varying the relative thickness of muscle layers and conductivity values are presented. Methods Simple geometries Simple 1D and 3D geometries (shown in Figure 1) representative of short sections of the small intestine were investigated. The gross geometry of these sections was described using cubic Hermite interpolation. Within each FGiegoumr et1ric meshes Geometric meshes. Simple geometric representations of an intestine co (...truncated)