Cellularity estimation forms an important aspect of the visual examination of bone marrow biopsies. In clinical practice, cellularity is estimated by eye under a microscope, which is rapid, but subjective and subject to inter- and intraobserver variability. In addition, there is little consensus in the literature on the normal variation of cellularity with age. Digital image analysis may be used for more objective quantification of cellularity. As such, we developed a deep neural network for the segmentation of six major cell and tissue types in digitized bone marrow trephine biopsies. Using this segmentation, we calculated the overall bone marrow cellularity in a series of biopsies from 130 patients across a wide age range. Using intraclass correlation coefficients (ICC), we measured the agreement between the quantification by the neural network and visual estimation by two pathologists and compared it to baseline human performance. We also examined the age-related changes of cellularity and cell lineages in bone marrow and compared our results to those found in the literature. The network was capable of accurate segmentation (average accuracy and dice score of 0.95 and 0.76, respectively). There was good neural network-pathologist agreement on cellularity measurements (ICC=0.78, 95% CI 0.58-0.85). We found a statistically significant downward trend for cellularity, myelopoiesis and megakaryocytes with age in our cohort. The mean cellularity began at approximately 50% in the third decade of life and then decreased +-2% per decade to 40% in the seventh and eighth decade, but the normal range was very wide (30-70%).