Relations between hydrodynamic and mechanical properties of a sphere.

Important hydrodynamic characteristics of a heart chamber are isometric pressures at operating distensions, compliances at operating distensions, and wall-displacement resistances at operating distensions. Wall-displacement resistance is the pressure change relative to the rate of cavity-volume change causing the pressure change. Another chamber characteristic is the dependence of wall-displacement resistance on distension. Equations were derived showing dependences of hydrodynamic characteristics on dimensions and mechanical properties of a thick-walled sphere whose inner and outer fibers are comparably stretched at operating distensions. Equations could be arranged so as to identify midwall elements whose enclosed volumes best express distension. If the appropriate midwall volume is used to express distension, then the fractional change of any intensive variable (pressure, apparent average stress, apparent midwall stress, wall-displacement resistance, volume-normalized wall-displacement resistance, apparent average viscosity, apparent midwall viscosity) depends simply on a property of the wall elements and fractional distension change or fractional rate of distension change. The apparent average stress or viscosity calculated with the assumption that the quantity is uniformly distributed is virtually the value of the quantity in the midwall element. These principles should be useful in characterizing normal and abnormal myocardium in situ.