To answer this question: use Figure 3.13 below, assume original Miner's rule is valid for bone tissue, and use the frequency of load as 1 cycle per second. a) Use a linear curve fit to derive and write the equation for compressive fatigue response (Include the graph, curve fit line, and the equation for your submission). (4 marks). b) For a modulus of 20GPa, estimate the total number of cycles to failure if a piece of cortical bone is subjected to these compressive load sequences: 80MPa for 100 cycles, 60MPa for 100,000 cycles, and 40MPa for the remainder of its life [8pts] c) Comment on the effect of three overloads on bone fatigue performance [4 marks] d) Repeat the above calculation with a modulus of 14GPa and compare the outcome vs the modulus of 20GPa [4 marks] Figure 3.13 Fatigue and creep behaviors of human cortical bone vs. time to failure. For fatigue loading, the ordinate on this graph can be converted to number of cycles by multiplying the time to failure by the frequency, which is typically one cycle per second for normal walking. Note that both creep and fatigue resistances are lower in tension, consistent with monotonic behavior. Data from Carter et al. (1981) Acta Orthop Scand 52:481-490 and Caler and Carter (1989) J Biomechanics 22:625-635