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Residual stress Force remaining in a body when all external loads are removed Gives rise to a residual strain (movement) which can be measured and used to estimate the degree of residual stress In arteries, residual strain can be quantified by measuring opening angle A O B

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Helps to balance forces within the arterial wall Controls the remodelling process by altering the local loading on VSMC Required to define the zero stress state A O B Why is residual stress important?

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0 40 80 120 11.11.2 Circ. Stress [kPa] Inner Outer Normalised radius No residual stress: inner / mean = 6.5 Residual stress: inner / mean = 1.4 Residual stress evens out the stresses in the vessel wall

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Pressurised tubes Heat Cool

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Steel rod Wet concrete in a mold Stretch steel while Concrete sets When concrete sets, tension in steel bends beam Beam withstands higher Load without bending 16 tons

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Cross and cupola 700 tons St. Paul’s Cathedral

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Residual strain in vegetables

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With thanks to Stephen Gottlieb

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1 2 4 3 7 5 6 1 mm 8 Rat aorta

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6050403020100 0 40 80 120 160 Age [weeks] Opening angle [°] Rat aorta No sex differences

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100806040200 0 100 200 300 Age [yr] Males Females Opening angle [ ° ] Human aorta

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Where does residual stress reside? Which part of the wall –Selective removal of layers, by lathing frozen specimens Which components of the wall –Selective digestion/destruction experiments, using enzymes to remove elastin/collagen and freezing to destroy muscle

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Artery lathe

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Fraction of vessel remaining Opening Angle [degrees] 1.00.50.0 0 100 200 -100 Material removed from outside Material removed from inside Material removed from both sides Localisation of residual strain Greenwald, S. E., et al. (1997). ASME Journal of Biomechanical Engineering 119: 438-444.

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Original After elastase treatment

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Original After collagenase treatment

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Original Minutes after freezing Months after freezing

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100806040200 0 50 100 150 200 FROZEN CONTROL Position (%) Opening Angle (°)

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0.00 0.25 0.50 0.75 1.00 1.25 CollagenaseElastaseFreezing Entire aorta Thoracic Abdominal OA ratio [Treatment/Control]

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Residual stress: conclusions Increases with age Greater in men than women Compressive at inner side of vessel wall Tensile at outer side Resides primarily in the elastic component –and to a lesser extent, in muscular component

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