Biomedical Engineering Reference
In-Depth Information
4.5 Intraluminal Pressure Calculation
Validation of the model is an important part of any multi-scale modeling study.
Therefore, it is important for the model to have an output that can be measured
experimentally. Clinically, antroduodenal manometry catheter is a commonly
applied method of recording to assess the patient's intestinal motility. The
assessment involves inserting a tube with pressure sensors through the stomach
and into the small intestine, sometimes for hours at a time. In order to compare the
model with experimental manometry recordings, we calculated the intraluminal
pressure due to the mechanical contraction of the intestinal model. For this initial
model, instead of attempting to deploy a computational fluid dynamics simulation
within the complex movement of the geometry, a relatively simple approximation
using Lamé's theory of stresses within thick-walled cylinders was applied. The
thick-wall formulation of Lamé's theory is typically used if the cylinder has a ratio
of wall thickness to internal diameter that is larger than 0.1 [ 38 ]; the ratio in this
model geometry was 0.3. The theory approximates the circumferential, or hoop,
stresses (r h ) in the wall of the cylinder using the internal (p i ) and external (p o )
fluid pressures and the internal (r i ) and external (r o ) radial values,
r h ¼ r i p i r o p o
r o r i
þ r i r o p i p o
ð
Þ
ð 28 Þ
;
r 2
r o r i
where r is the coordinate corresponding to the radial location of this stress value.
These parameters are visualized in Fig. 9 . The derivation of Lamé's equation can
be found in [ 42 ].
Assuming no external pressure, rearranging for internal pressure gives,
p i ¼ r h r 2
r o r i
ð 29 Þ
r i
r o þ r 2
Stress values in the fiber, sheet and sheet-normal directions can be calculated at
each gauss point and at each time step of the simulation. The stresses in the fiber
direction at the inner surface of the intestinal model correspond to circular wall
stresses at r ¼ r i because the fibers on the inner surface of the intestine model are
aligned in the circumferential direction. Intraluminal pressures calculated using
stresses at r ¼ r i can therefore be expressed as,
r o r i
p i ¼ r gauss
ð 30 Þ
r o þ r i
where r gauss are the fiber stresses at the innermost gauss points in the simulation.
Radius values can be calculated by taking the distance between the innermost
gauss
point
and
the outermost
gauss point
at corresponding
circumferential
coordinates.
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