We demonstrate the feasibility of high resolution models of bidirectionally coupled cardiac electro-mechanics which resolve cardiac anatomy at a para-cellular resolution.A novel algebraic multigrid method is presented,adapted for non-linear mechanics,which is shown to be strongly scalable up to 8k cores when using a human whole heart four chamber geometry model.Benchmark results demonstrate that a single heart beat can be simulated in about 1 hour minutes at full anatomical and biophysical detail.