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

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?

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

Pressurised tubes Heat Cool

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

Cross and cupola 700 tons St. Paul’s Cathedral

Residual strain in vegetables

With thanks to Stephen Gottlieb

mm 8 Rat aorta

Age [weeks] Opening angle [°] Rat aorta No sex differences

Age [yr] Males Females Opening angle [ ° ] Human aorta

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

Artery lathe

Fraction of vessel remaining Opening Angle [degrees] 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:

Original After elastase treatment

Original After collagenase treatment

Original Minutes after freezing Months after freezing

FROZEN CONTROL Position (%) Opening Angle (°)

CollagenaseElastaseFreezing Entire aorta Thoracic Abdominal OA ratio [Treatment/Control]

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