Transient integral boundary layer method to calculate the ...

BioMedical Engineering OnLine 2006, 5:42http://www.biomedical-engineering-online.com/content/5/1/42 Deformation Figure 3 cross-sectionDeformation cross-section. This figure illustrates the deformation geometry of a circular, linear elastic tube neglecting thebending stress inside the wall. Cross-section B - B (left) shows circular expansion under pressure and the cross-section C - Cillustrates the geometry under external deformation (right). The equilibrium cross-sectional area A d is shaded in light grey,while the perturbation area A' is shaded in dark grey. The dashed lines indicate expansion under pressure.ity in axial direction. The volume flux across a given sectiontherefore is q (x, t) = A u.As shown in the angiography 1 and Figure 2 the coronaryarteries in myocardial bridges are structured by severalwall deformations. Their number, degree and extensionmay independently vary with time, so that the axial curvatureof the arterial wall for each of the n = 1...N myocardialbridges in series is characterised by N functions. Thedeformation is specified by a parameter ζ, defined as ζ =R d /R 0 , which is chosen in the stenosis n to vary with timeas( ) +1ζn ( t) = ζdiastole −ζsystole ( gn 1)+ ζsystole,( 1)2where g n (t) are periodic functions describing the temporalcontraction of the muscle fibres. ζ systole and ζ diastole are fixedgeometrical parameters between 0 and 1, specifying thedegree of systolic and diastolic deformation respectively.We note that in the centre of the deformation ζ (x = x s2 ) =ζ 0 = R d /R 0 , i.e. the degree of deformation increases withdecreasing ζ 0 and consequently ζ systole