Limits...
Effects of gastrointestinal tissue structure on computed dipole vectors.

Austin TM, Li L, Pullan AJ, Cheng LK - Biomed Eng Online (2007)

Bottom Line: 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.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Bioengineering Institute, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand. t.austin@auckland.ac.nz

ABSTRACT

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.

Show MeSH

Related in: MedlinePlus

Transmural potential gradients. Transmural transmembrane potential for different muscle layer ratios at two time instances corresponding to the two dipole magnitude maxima shown in Figure 4. The model with muscle layer ratios of 2:1:5 shows an asymmetric profile across the wall, while the 2:1:2 models is symmetric. The asymmetric profile causes the dipole vector to be orientated at an angle relative to the principal direction of the slow wave. A 2:1:4 ratio yields a similar asymmetric behaviour to the 2:1:5 ratio but less pronounced.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC2117001&req=5

Figure 5: Transmural potential gradients. Transmural transmembrane potential for different muscle layer ratios at two time instances corresponding to the two dipole magnitude maxima shown in Figure 4. The model with muscle layer ratios of 2:1:5 shows an asymmetric profile across the wall, while the 2:1:2 models is symmetric. The asymmetric profile causes the dipole vector to be orientated at an angle relative to the principal direction of the slow wave. A 2:1:4 ratio yields a similar asymmetric behaviour to the 2:1:5 ratio but less pronounced.

Mentions: In Figure 5, the transmural potential at the bend was plotted for two time periods which corresponded to the two maximum dipole magnitudes shown in Figure 4. These two times corresponded to instances when only the depolarisation or repolarisation fronts were present in the specimen. It was evident that unequal thicknesses of the smooth muscle layers led to asymmetrical transmural potential gradients on both sides of the ICCs, and hence a net transmural potential gradient across the wall. Due to unequal element volumes at the bend, the transmural potential gradient at the bend significantly contributed to the orientations of the dipoles. For the asymmetrical model, when the dipole was at a maximum magnitude, there was also a significant transmural gradient at the bend, resulting in an orthogonal dipole component.


Effects of gastrointestinal tissue structure on computed dipole vectors.

Austin TM, Li L, Pullan AJ, Cheng LK - Biomed Eng Online (2007)

Transmural potential gradients. Transmural transmembrane potential for different muscle layer ratios at two time instances corresponding to the two dipole magnitude maxima shown in Figure 4. The model with muscle layer ratios of 2:1:5 shows an asymmetric profile across the wall, while the 2:1:2 models is symmetric. The asymmetric profile causes the dipole vector to be orientated at an angle relative to the principal direction of the slow wave. A 2:1:4 ratio yields a similar asymmetric behaviour to the 2:1:5 ratio but less pronounced.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2117001&req=5

Figure 5: Transmural potential gradients. Transmural transmembrane potential for different muscle layer ratios at two time instances corresponding to the two dipole magnitude maxima shown in Figure 4. The model with muscle layer ratios of 2:1:5 shows an asymmetric profile across the wall, while the 2:1:2 models is symmetric. The asymmetric profile causes the dipole vector to be orientated at an angle relative to the principal direction of the slow wave. A 2:1:4 ratio yields a similar asymmetric behaviour to the 2:1:5 ratio but less pronounced.
Mentions: In Figure 5, the transmural potential at the bend was plotted for two time periods which corresponded to the two maximum dipole magnitudes shown in Figure 4. These two times corresponded to instances when only the depolarisation or repolarisation fronts were present in the specimen. It was evident that unequal thicknesses of the smooth muscle layers led to asymmetrical transmural potential gradients on both sides of the ICCs, and hence a net transmural potential gradient across the wall. Due to unequal element volumes at the bend, the transmural potential gradient at the bend significantly contributed to the orientations of the dipoles. For the asymmetrical model, when the dipole was at a maximum magnitude, there was also a significant transmural gradient at the bend, resulting in an orthogonal dipole component.

Bottom Line: 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.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Bioengineering Institute, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand. t.austin@auckland.ac.nz

ABSTRACT

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.

Show MeSH
Related in: MedlinePlus