TAILIEUCHUNG - Biomedical Engineering 2012 Part 15

Tham khảo tài liệu 'biomedical engineering 2012 part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 552 Biomedical Engineering regarded as a thin cylindrial shell positioned between two rigid and parallel planes that is tonometer and underlying bone. The undeformed radius of the artery is r and the distance between the planes is 2b. While hold-down pressure increases arterial wall is deformed and the distance of planes decreases. And the total external force and the length of contact can be formulated as a function of the distance b. The solution for the end shear force V and half length of flattened section t can be written as a function of planes separation b V b b2 EI 1 TT b t b -- r - V 1 2 2 where E and I represent the Young s modulus and the moment of inertia of the artery respectively. If the dimensions and forces acting on the ends of the flattened wall segment are known the contact stress ơc can be calculated. When the segment of artery has changed shape from cicular to straight the flexure equation can ben written as a difference in curvature as equation 3 . 1_1-- M _ d r1 r EI AG dx 3 where r initial radius r1 radius after distortion M applied bending moment I moment of inertia for flattened wall cross-section a a geometric constant A crosssectional area of flattened wall G shear modulus of arterial wall E 2 1 v u Poisson s ratio. Then considering the balance of shear forces and bending moments in a radial plane of the vessel wall dM dx-V 0 is given and let P2 AG a EI equation 3 can be modified as d M - PM -r . 4 dx2 r Then M x s general solution can be expressed EI M x C1ePx C2e-Px 5 r As V x can be obtained by the differential of M x the constants C1 and C2 are dtermined from the shear foce relations V x cpepx - C2e-Px 6 Tonometric Vascular Function Assessment 553 Considering the contact force per unit length q x and substitition q x dv dx 0 with contact stress defined as ơc x -q x AL then the relationship between contact stress and deformed distance is given cosh fix _ r b fi 7 Sinh fit In Fig. 3 the computed contact stress .

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